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MINEEALOGY.

J.*'Hr90LLINS, F.G.a,

AnUuH of " A. Handbook to Uu Ulnenlag; at Oomvall and DsTon,"

"A Tint Book at Jliatnlatj," Bin.

Booonu? S«TetU7 to thaUliunlaguiilSooltt; of Qmt Britain uid Inland, dto.

Vol. L— the OENEEAL PRINCIPLES OP MINERALOGY.
mt^ 579 latttliBtiJins.

LONDON AND GLASGOW:

WILLIAM COLLINS, SONS, & COMPANY.

1878,

Science I llifAf Y

367

X73

PEEFACE.

In preparing this work for the press, I have endeavoured
primarily to keep in view the needs of the same class of
students as my Fvrzt Book of Mineralogy was written for,
viz., practical working miners, quarrymen, field geologists,
and students of the Science Classes in connection with
the Department of Science and Art. I believe the work
properly studied will enable its students to pass the €k>vem-
ment Examinations with credit; but I hope it will do much
more than this, and that my readers will become practical
^ineralogiats, able to detemine the nature of suoli unknown
Species of minerals aa may fall in their way, and to appreciate
the relations borne by the science of Mineralogy to the sister
sciences of Chemistry, Geology, Metalluigy, and Mining. I
have endeavoured throughout to use plain language, and in
dealing ' with Crystallography, I have remembered that a
majority of my readers were not likely to have had much
mathematical training. Consequently it has been necessary
in some instances to adopt somewhat roundabout methods
of definition or descriptions. The liberality of the Publishers
in allowing me such a very large number of woodcuts, has
much assisted me in this dilution.

Believing as I do that the Crystallographic system of
Professor Miller is the best yet invented, I have to some

4 PBEFACB.

extent led up to it through the apparently simpler but less
perfect system of Naumann, which is adopted by many
science teachers^ and which I myself used in the lirst Book
already mentioned. In works of this character there can of
course be very little that is absolutely new, but I have
endeavoured to condense or to simplify much of what has
already been written. Among works particularly made use
of, I may mention those of Kicol, Brooke and Miller, Mitchell
(in Orr^s Circle of the Sdericea), and Dana.

My thanks are due to Mr. B. Kitto, F.G.S., of Camborne,
for his valuable assistance in correcting many of the proof
sheets.

This volume will be followed by another (now in the press),
giving detailed descriptions of most of the minerals known
to science.

In conclusion, I would strongly urge teachers of Miner-
alogy not to attempt to teach either from this book or any
other without constant reference to models, and especially
to actual SDecimens of the minerals referred to.

J. H. a
67 Lbxok Street, Truko,

October 1877.

CONTENTS

CHAPTER L
Intboduction, •...,, 9

CHAPTER IL
The Forms of Minerals— Imitative Forms, etc., • .11

CHAPTER IIL
The Gteneral Properties of Crystals, • • • • 18

CHAPTER IV.
Representations of Crystal Forms, ... . .27

CHAPTER V.
Holohedral Forms of the Cnbical System, . • • 33

CHAPTER VI.
Hemihedral Forms of the Cubical System, • . . 39

CHAPTER VIL
Combinations of Cubical Forms, . . . . 43

CHAPTER VIIL
The Tetragonal System, ...••• 55

CHAPTER IX.
Hemihedral Forms of the Tetragonal System, « • . 6

6 CONTENTS.

CHAFTEBZ.

PAGS

Tetragonal Combinations, • • • • • 65

CHAPTBE XI
Tetragonal Combinations (Hemiliedral), • • • 72

CHAPTER XII.
The Kbombio System, •••••# 76

CHAPTER Xm.
The Oblique System, 93

CHAPTER XIV.
The Anorthic System, • • • • • • 102

CHAPTER XV.
The Hexagonal System, • • • • 107

CHAPTER XVL
On Macles and Irregular Crystals, • • • 120

CHAPTER XVIL
On Dimorphism, Pseudomorphism, and Petrifaction, '• • 134

CHAPTER XVm.
On Measuring Crystals, • . . « • 140

CHAPTER XIX.
Physical Properties-^Cleavage, , • • • • 146

CHAPTER XX.
tliysical Properties— Structure, • • • • 150

OpKYEKtSL 7

■

CHAPTER XXL

PAOV

Physical Properties^Magnetiimy eta, • • .157

CHAPTER XXIL
Optical Properties— Colour, • • • • • IGO

CHAPTER XXIII.
Optical Properties — Refraction and Polarization, • • 164

CHAPTER XXIV.
Chemical Characters— Taste, Odonr, etc., • • 172

CHAITTER XXV
Chemical Characters—Blowpipe Analysis, • • • 178

CHAPTER XXVL
Distribution and Paratcenesis, • • • • • 1S8

CHAPTER XXVn.
On Artificial Minerals. • . • • • • 191

Examination Questions, • • • • •197
Index, 203

?

MINERALOGY.

THE GENEEAL PRINCIPLES OF MINERALOGY.

CHAPTER L
INTRODUCTION.

1. '* Minerals are natural, homogeneous, inorganic bodies."
This definitioii includes many substances not usually regarded
as minerals, such as vMter in its several forms of solid, liquid,
and gas; air; the gases given off from volcanoes or from
fissures in earthquake regions; and Hquids Uke sulphuric
acid and naphtha which are naturally produced in certain
districts.

A strict application of the definition would exclude all
substances of vegetable origin, such as peat, coal, and amber,
but it has been found convenient to include descriptions of
these and a few other similar substances in mineralogical
treatises, and we have not departed from this practice in the
present volume.

2. Bocks are usually mineral svbatancea but not miv^raih.
Some, like granite, gneiss, and dvanite, are aggregates of
several distinct minerals; others, like dolomite, serpentine, and
gypswm, are simply impure massive forms of the minerals of
the same names. The following list of the minerals trhich
most frequently enter into the composition of rock-masses or
of veinstone, occupying fissures in such ma^es— ro(^/amer«
as they may be termed — ^will be useful to the student.

10

MlNE!tlAtOG¥.

A.^MiNSRAL3 Common
Quarts
The Felspars.
Kaolin.
The Micas.
Toarmaline (Schorl),
Chlorite.
Garnet.

Amphibole {ffomhlende).
Pyroxene {AugUe),
Seri>entlne.
Olivine.
Gypsum.

B.— Minerals Common

IN Bock Masses.

Apatite.

Calcite.

Dolomite.

Halite {Rock Salt).

Sulphur.

Graphite.

Magnetite.

Hematite.

limonite.'

Chalybite.

Pyrites.

CoaL

AS Veinstones.

limonite.
Hematite.
Chalybite*
Chlorite.

Galena.
Calcite. Chalcopyrite.

Barytes. MispickeL

Fluor. Pyntes.

The study of rocks belongs to Geology^ of which science
Mineralogy may be regarded as an important branch.

3. Minerals have many peculiar mecluinical, opttcdl, and
other physical characters. Thus, some like quartz and the
diamond are very hard, others like talc and graphite are very
soft. Most minerals at ordinary temperatures are solid, but
some few, like mercury, naphtha, and water, are liquid, and
others like carbonic acid are gaseous. The complete study
of these properties belongs to Physios, but a considerable
portion of the present volume will be devoted to the con-
sideration of these properties.

4. Minerals have many chemical properties; thus, some
like witherite are poisonous, others like rock-salt form
valuable additions to food, or like mercury are of great value
in medicine. Some are fusible, others infusible ; some are
soluble in water or acids, others quite insoluble. The com-

i)lete study of these properties belongs to the science of
Ihemistry, and Mineralogy may be re^urded as the connect-
ing link between Chemistry and Geology.

6. General Mineralogy may be divided, for greater con-
venience of study, into sections as follows : —

1. Form.

2. PHTStCAL CHAAAOTERS.

d. CHEiaoAL Charaotkrs.

4. Discrimtnaton of Minerals.

5. Classification.

6. Distribution.

7. Pabaobnesis*

CHAPTER n.
OF THE FORMS OF MINERALS— IMITATIVE FORMS, Era

6. The researches of Graham and others have shown that
inorganic matter may exist in two perfectly distinct con-
ditions, known respectively as erystaUoid* and coUoid,\
The same portion of matter may be at one time crystalloid
and another colloid, the difference being one of condition not
of composition. Thus rock-crystal consists of crystalloid
silica, but if a fragment be powdered, fused with carbonate
of soda, dissolved in water, and precipitated by hydrochloric
acid, the precipitated silica will now be in the colloid state.
When in solution, crystalloids differ from colloids in some
very important particulars, and on passinfi; into the solid
far^ thidifferenL ai» still moie evident^

7. Colloid minerals are few in number. They are totally
devoid of cleavage or distinct internal structure, but they
usually break with a very perfect conchoidal fracture. They
occasionally, but not often, occur in what are called imitative
forms, but are usually amorphotis or without definite external
forms. { As examples of true colloid minerals, we may
mention opal and obsidian.

8. Crystalloid minerals are very numerous, they include,
indeed, the great majority of mineral species. They may be
either crystaMised, crystalline^ or crypUxyryatoMine,

a. Or^rstallised mitierals are those which occur in definite
geometrical forms, the properties and peculiarities of which
will be dealt with in much detail in future chapters.
Ordinary roch^rystal is a perfect example of a crystallised
mineraL

* Ico-llke, from Kfd^faXUs {crydaUos)^ ice; i73#s (6u2(w), resembknce*

t Gltte-lik«, from KtXkn (eo22e), glue; and uht.

$ Formlofls, from », without) and ft»p^n {morphe), fomit

12 UIKE&ALOOY.

b. CljBtalline minerals are Buch as have the peculiar inter-
nal Btructore observed in those vhich are crystallised. They
consist, indeed, of a multitude of crystals confusedly crowded
together, so tlu^t the external geometrical form is lost or dis-
giused. Thecavitiesor"Tugha" of such aggregates, however,
often display distinct crystals. The kind of quarte known aa
enM-anir»6 »par affords a good example of a crystaUised
minersL

c Ciypto-oryBtaUina * minerals are those in which the
crystalline structure la so minute that it is not ordinarily
observable, but it may be detected in suitably prepared
specdmens when examined under the microscope:! Chalcedony
eioA. agate are good examples of crypto-crystalline minerals.

9. Many ctystalline and crypto^jrystalline, and some
amorphous minerals, occur in what are known as imUattve
fonns. The chief of these are the following ; —

Rg. 1. — GLOBtTLiS.

a. Olobnlar, fig. 1. — This form is often seen in tcaveUUe,
prehnite, and other minerals. The author has specimens of
pyrites from the chalk of Dover, and of pyritous blende from
C^nnwall, which are detached spheres. On breaking a glob-
ular mineral, it is almost always seen to be composed of a
multitude of indistinct crystals radiating &om the centre,
and sometimes the out-side of the sphere is roughened by the
projecting points of these crystals. Occasionally the true

" lairrrtt (eryptoa), concealed.

t Tnuuipwent miuends may be cat into tUn alicea and examined

THE FOBUS OP HIHERAU. 13

erystftl form of these terminations ma; be obnerred, but
usaaHf they are indistmct

b. Benifonn {kidney-iht^ped), fig. 2. — This form ia not
mifrequentlr met with in nodules of iron pyriUs, or other
minerals wMch occur imbedded in clay or mud. Some kinds
of red and brown hematite are called kidney iron ttovi their
occurrence in tiiia form.

Fig. 2— Kknitoiiv.
e. Botiyoidal {ffrap^like), fig. 3. — 'Dus form is often seen
in that kind of ehak<^yrUea known as bUstered copper ore.

Fig.3.— BoTBTonui.

d. Hunmillary, fig. 4. — ^This form is often seen in mala-
ehita and UiaUred copper on;

e. Oonlloidal (coraliiix), Gg. 5. — ^Tbia structure is ob-
servable in chalcedony and aragonito, especially in specimens
from Styria. It sometimes occurs in connection wiik earthy
deposits of iron ore, when it ia called j((M/Wt, or the flower
of iron.

/ Oone in Gone, fig. 6. — This Btmcture is often met with
in iron ores from the coal messiires. It consist of a series of

MINEKALOOY.

fibrous concentric conical masses, the points of the cones
meetii^ together, or Bometimes interlaced aa shown in the
figure.

Fig. 4. — UAUHILLAlty.

Fig. 5. — CoBALioiDAL. (Froma Fhotograph.)

Fig. 6.— Com Di Cone. (From a Photognqib.)
g. Stalaotitic (ieiole-Bhaped), fig. 7. — GhcJ^edony, caleite,
and barytes often occur in this fonn. Sometimes the stal-
actites are hollow, sometimes solid; but in stalactiteB of caleite
and barytes, a cross-aectioa almost alw&ys reveals a stnictnre

THE FORUS OF KINEBAU,

counting ot fibres radiating from the centre, and the same
thing is visible in properly prepared slices of chalcedony,
when examined under the microscope.

Fig. 7 — STAiAPrnro.

Fig. 8.— Vbbtical Secttoit op a STAixcmrx or Calcite, ibowing
BDOoMedve layera of deposited matter. (From a f hoto^^qdk).
10. It is probable that most, if not all, of tbe abore^eBCtibed
imitative forms are the result of deposition frtim solution, at
any rate this ia known to be the casQ in some instances.
Thus, stalactitea of calcite, or carbonate of lime, may be seen
in process of formation in caverns in most limestone districts,
ond they are very frequently formed under bridges or tunnels
which have been built with lime mortar. The process of

16 WKKRALOaT.

fomution ia as followa : rain wtder conttuning oorbonio
acid in soluticHi in filtering through limestone, mortar, or
other material containing carbonate of lime dissolTOS a part
of it. On becoming again exposed to the air drop by dirop,
part of the oarbonio acid ia given off, part of the water
evaporates, and part of the carbonate of lime ia deposited.
A stalactite onoe formed the water naturally descends to it«
lower end before falling off, and it is there ttiat the greatest
amount of carbonate of lime will be deposited, and in this
direction its growth will be most rapid, although a small
quantity of solid matter will continue to be deposited on the
sides of the stalactite, so producing the concentric structure
shown in the vertical section of a stalactite, fig. 8, and in
the cross-section, fig. 9. The radial
structure appears to be of later
origin; it is really due to an incipient
crystallization set up within the

The water dropping from the

Fig. 9.— CRoas-SBonos oh stalactite will still contain some

UNI A B, fig. 8, gbowina; carbonate of lime in solution. This

concentric and raduu will be deposited on the ground

t^rf?!' *^^°^*^''°" beneath, when the conditions are

*°S"'V^. favourable, forming what ia known

as ttalagmile. A cross-section of

stalagmite, however, will differ from

that of a stalactite, owing to the

tendency which the drops of water

have to spread themselves out. If

the supply of water be abundant, a

sheet of stalagmite wiD be formed

if only a little &11b, a plUar of

V! IA T»-" ...._ stalagmite will gradually rise to-

^JJo^iS^'S"™ '7* «.= rtJrfte aboy.; but ia

rLooR or A LtKKSTONB ^ cases the separate la3rers will be

Cavekn, ihowing lajets of about equal Udcknesa l^iroughout,

of equal thioknetw. as shown in fig. 10.

Many other substances besides carbonate of lime are thus

deposited &om solution. In the old workings of several

Cornish tin and copper mines, the writer has &equently seen

THE FORMS 07 MINERALS. 17

long stalactites of oxide of iron depending from the roof, and
stalagmites of the same material rising from the floor to
meet them. Stalagmites of malachite were seen in process
of formation in l£e mines of Bussia, by Sir Eoderick
Murchison.

11. The crystalline structure sometimes observable in the
imitative forms already described, is probably the result
of a secondary action of the crystallising forces, following the
actual formation of the solid mineral. There are, however,
other imitative forms which are merely irregular crystals or
crystalline aggregates, and in the formation of which the
crystallising forces appear to have been concerned from the
first. These are the so-called capillary and wiry forms ob-
servable in ruitive silver^ the mossy and lec^y forms seen in
native copper^ the dendritic markings of oonde of manganese,
the reticulate groupings characteristic of mmmtain leather,
and the stellate groups of crystals often met with in stUbite
and other minerals. These will be further described in a
future chapter.

13—1

CHAPTER in.

OF THE GENERAL PEOPEETiES OF CETSTAL8.

12. Many minemlA ooouf naturally in forma bounded by
plane surfaces, having peculiar geometrical relatiouB to each
other, IThese are called " cryBtals," the plane BurfaoeB are
termed "planes" or "faces," iJie lines formed at the junction
of any two such planes bm " edges," and the points fonned
by the meeting of any three or more edges are called " solid
anglea."

Fig. 11, Fig. 13.

Every plane in a crystal has a definite inclination or slope
in relation to every other plane, except suok as may be
parallel to it. These mutual inclinations are quite indepen-
dant of the size or general form of the crystals, and tiiey are
constant for similar planes even in different crystals of the
same mineral, as is shown by meafiurement with the goni-
ometer,* Thus, if figs. 11 and 12 represent crystals <tf fiuor,
the planes a a will in each case be inclined 90° to each other,
and the planea o a 109° 28', notwithstanding the difference
in their appearance and in the general aspect of the ciystal.
The mode of actual measurement is resorted to wfiea the
ciystal form of any specimen is to be determined for tlie
firat time; but the geometrical relations of the planes are
best understood by referring them to certain imaginary lines
• }wii'a (sonio), an angle; pirftt {melroii), a. weMnrft

THE OENSSAL PBOPEBTIES OF CBTSTAL8.

19

termed axes, which are supposed to exist within every
crystal.

To understand the higher branches of crystallography re-
quires a good deal of mathematical knowledge and slall, but
the attempt has been made to write the crystallographic por-
tion of this volume in such a manner that a very moderate
acquaintance with elementary geometry and wil^ algebraic
signs and formulae, may suffice on the part of the student.

Fig. 13.

IS. We have said that the planes of all crystals are
referred to their axes. Fig. 13 will help the student to
realise what is meant by this statement. Let A - A, B - B,
C - C, represent three axes of a ciystal, cutting each other
in the centre, O. In the figure, the axes are drawn in per-
spective, but they are in this instance supposed to be of equal
length, and at right angles to each other. The semi-axes
OA, O - A, OB, O - B, OC, O - C, are called the parameters.
Let us suppose one plane of the crystal to be so situated
as to cut the three parameters OA, OB, 00, at their ex-
tremities A, B, 0, which, it must be remembered, are equi-
distant from the centre. It is evident that such a plane
will have a definate inclination or slope. Siippose, further,
a plane to exist cutting the three semi-axes in the points
^1 ^i ^v "^^^^ ^-^ ^Iso equally distant from the centre O.
Such a plane will be smaller than that cutting the points

t

It

20 HINEBALOOT.

A, By C, but it will be evidently parallel to it, since the
distances Oa^ 06^ O^ are equal. A little consideration will
show that whatever the absolute distances from the centre
may be, so long as they are equal, no new slope or inclination
is possible; the planes so situated will be parallel and similar,
and any sign devised to express the slope of one will indicate
the slope of all. A plane, however, cutting the points o^ b^ Cj
will have quite a different slope.

We will now suppose a plaiie to cut the semi-axes O - A,
- B, - 0, in the points - A, - B, - C. This plane will be
parallel to one cutting the points - a^ - 5^ - c^ ; and also to
the planes already described, but on the opposite side of the
centre. If, however, we have a plane cutting the semi-axes
O - A and O - B in - o^ - 6^, but the axis O - C in the point
- Cg, it is clear that the slope of this plane will be quite
different from that of the planes just described, and parallel
to the plane a^ b-^ e^ This slope, however, like the others,
evidently depends not on the absolute lengths of the portions
Oa^ Obi ^^p ^^^ upon their proportions or ratios, and so
with all other planes which we may refer to the same axes.
As there are three axes, and each or all of them may be cut
at any points in any ratios, it is evident that an infinite
number of planes is possible, but that the slopes of all are
fixed so long as we know those ratios. Fortunately, in any
particular mineral, the number of planes is limited by the
fact that the ratios are always comparatively simple and not
very numerous.

14. Elements of CrystalB. — ^In most crystals the planes
are referred to three axes, but in one large class they are
sometimes referred to four. The axes may cut each other at
right angles or at any other angles. The number and
relative situation of the axes, and the ratios of the parameters,
together constitute what are called iha elements of a crystal.

15. Crystallographic Notation. — ^Many systems have been
at different times devised for indicating the relations of the
different planes to the axes, but of these it is only necessary
for the student to be acquainted with three at present, those
used by Professors Mitchell, Naumann, and Miller. A brief
outline of ISTaumann's system is given in the " First Book of
Mineralogy,'' forming one of this series of text-books, and

CftTSTALLOOBAPmO HOTATION.

21

some further explanations will be given hereafter as occasion
may arise. The symbols adopted throughout this work in
describing the various forms, are those of Professor Mitchell,
except when the contrary is stated. They are modified from
those used by Miller, and generally differ but little from
them. Naumann's symbols will also be given in many cases.
In order to imderstand the symbols of Mitchell and Miller,
we must refer to fig. 14. Let - A O A,-B O B,-C O 0,
represent three axes of a crystal cutting each other in the
centre O. Different planes will cut these axes in different
ratios ; but in all crystals some planes will be of more im-
portance than others, and these are regarded as belonging to
primary forms.

B

ao^ —

-A ^

lio

f

^^

-B

*^ .c^y c*

nr

1>Z

T

— ^ a

Kg. 14.
Suppose one such primary plane to cut the axes in the
points a^ 5^ c^, then Oa^ 05^ Oc^ may be regarded as the
paramet^ of the form in question. Now on the line
- A O A, take Oaj = J Ooj, Oa^ = J Oa^, and so on; making
as many points as may be necessary towards O. Take, also,
Oa^i^Oa^y 0(i-2 = Oa2, Oa-g-Oaj, on the other side of

22 MINERAL0G7.

the centre. * Further, suppose Oa^ to' exist by prolongmg
the line - A O A in both directions to any infinite distance.
Determine similar series of points in -BOB^ -00 0, as
shown in the figure.^

All the planes of a given crystal will now be parallel to
one or other of the planes passing through three of the^
points so determined.

16. In Professor Miller's system of Notation, the symbol
111 is used for any plane paiullel to that cutting the axes in

Oi hi e^y 122 for these parallel to o^ &2 ^2 ^^^* ^^^ ^s ^1 ^>f^^
so on; the numbers 111, 122, 313, are termed irhdtces. When
any of the points referred to have negative signs, the corre-
sponding indices have negative signs placed over them. Thus,

the indices of a plane parallel to a - ^^ &2 ''2 '^'^ ^ ^^^9 ^^^
ofa-^bo ^"z '"^ ^ ^^^' Iii<i^ces higher than 6 are veiy
rarely required.

When planes have to be indicated the precise values of
whose indices are not known, or where a general symbol is
required for any set of planes, the letters hkl are used as
general indices, and either of these letters may stand for any
whole numbers, or for zero. Parallel and opposite planes
have the same indices but different signs.

When one of the indices of a plane is zero the plane is
parallel to the corresponding axis, since the point in which
the plane intersects the axis is infinitely distant. When
two of the indices are zero the plane is parallel to the cor-
i^sponding two axes.

17. Sphere of Projedtton^ — ^A different mode of indicating
the geometric relations of the planes is sometimes adopted
by crystallographers for more convenient calculation. The
(oentre o, fig. 13, is regarded as the centre of a sphere. The
three axes will of course meet the sphere in six points, called
the " poles of the axes." This sphere is called a " sphere of
projection."

18. Normals^— Prom the centre O, radii are supposed to
be drawn, meetiilg each plane perpendicularly. It is evident
that the radii so originated w£Q have fixed inclinations

* Maay stadents will be greatly aided by taking three thin rods of
wood, fattened to j;ether in the centre, and inarlnng upon them with
bompfysfles the vanons pomts referred to in the text.

eoMbtNAftom a

to each other. They are called '^normab'' to the planes,
and the points in which they meet the sphere of projection
are called the '* poles" of the corresponding faces. A face
and its pole may be indicated by the same symbol.

The angle included by any two normals is the supptement
of that included by the two corresponding faces, so that it is
easy to determine the angles of any two normals^ when that
of the corresponding faces is known, or vice verses Thus,
if the angle included by two planes be 110^, that of their
normals will be 70^

19. Zones. — ^It frequently happens that several faces of a
crystal intersect each other, or would do so if they were
pi^uced until they met, so that the Intersections form
parallel lines. Such a series of faces is called a '^ zone.'*
The normals of the several faces in a zone lie in one plane,
Called the '* zone^plane,'* and the poles all lie in a great circle
of the sphere of projection, called the ''zone-circle.'' A
line passing through the centre of the zone^plane, and cutting
it at right angles, will be the '' zone-axis.'* The zone«zis is
parallel to all the fsicea of the zone* A face may be common
to two or more zones, when its normal ^^friH coincide With the
intersections of the several zone-planes*

20. A Form in crystallography is a figure bounded by a
series of planes, having similar indices, differing only in
their signs* Forms may be indicated by the symbol of any
one of their faces. HOlohedral^ ot ''pleno-tesseral'* forms
are those in which the full series of planes having given
indices are pl^sent Hemihedralt of "semi-tesseral'^ forms
are those in which only alternate faces ot groups of faces are
present In Tetartohedral t forms only one-fourth the full
number of faces is present*

21. Combinations* — ^Any figiM bounded by planes be-
longing to more than one form> is called a '' combination.'^
Thus, dg- 15 is a form called the octahedron ; fig. 16 is the
form known as the cube. In figs. 17 and 18, which are said
to be combinations of the cube and octahedron, the planes of
both forms appear, and are indicated by corresponding letters.

* tx»t ihohs), whole ; Hf* {hedra), a seat or plane.

t nfu {himi)f half ; and U(«<

Z nra^Ms {teUxrtOf), fourth ; and t^K^

These figures serre also to illnrtrate the differences in ap-
peareooe wUch m&j exist when the same planes are more
OF less developed.

Kg. 17. Pig. 18.

22. SystemB of CiysUl Forms. — It is usual to group all

crystala under six systems, which have been Beverallj named

as under. The firsb of these names is that which will be

adopted throughout in this work : —

1. Cabioal, (OetahedrtU, Teuerai, Tessular, Regviar, Mono-
metric, etc.)

2. TetrafTOQftli {Pyramidal, 2 and 1 asewi, Dimetrie, etc.)

3. BhomMo, (Priamatic, OrtAott/pe, 1 and 1 aadal, !Pn-
melrie, etc.)

4. Obliqu^ (MoTKcUrUe, Semiorlholr/pe, 2 and 1 tnem-
bend, etc.)

5. Anorthio, {TruUnic, Doubh OUique, Anorthotype, 1
and 1 membered\.

6. HeZBgOHU, {RhombohednU, 3 aTid 1 axial etc\

The elements of the siz STstems (see Art. 14) are aa
follows : —

Cvbteai. — ^Three axes at right angles to each other, the
axes (consequently the parametera or eemi-axes) eqnal in
length. As the axes ars equal to each other, and similarly

SYSTEMS Of CBTSTAL FOItMS. 25

related in all cubical minerals, the '^ elements" are said to be
" fixed."

Tetragonal. — Three axes at right angles. Two equal to
each other, called lateral. The third or principal axis is
variable ; in some pyramidal minerals it is longer, in others
shorter than the laterals. There is consequently one
"variable element" in this system, viz., the proportion
existing between the length of the "principal" and "lateral"
axes.

Rkomhic. — ^Three axes at right angles. All unequal in
length, and the relative lengths varying in different miaerals.
One is selected as the principal, the others are called lateral.
The longer lateral axis is the "macro-diagonal,"* the shorter
the ."brachy-diagonal."t Thus there are two variable
"elements" in this system, viz., the ratios respectively of
the "macro" and "brachy" diagonals to the principal.

Oblique. — ^Three axes, two at right angles, the third in-
clined at different angles in different systems; relative lengths
variable in different minerals and usually all unequal. One
of the two which are at right angles is taken for "principal,"
that at right angles with it is termed the " ortho-cQagonal," J
that which is inclined is the " clino-diagonal." § There are
consequently three variable " elements " in this system, viz.,
the ratios of two axes to the third, and the inclination of the
" clino-diagonal " to the " principal."

Anorthic. || — ^Three axes: all variable in length and usually
unequal; all inclined at different angles. Thus there are
four variable "elements" in this system, viz., the ratios of two
axes to the third, and their inclinations to each other. Either
of the axes may be taken as principal, when the other two
will be lateral The longer lateral maybe tei-med "macro-
diagonal," the shorter "brachy-diagonal" as in the rhombic
system.

Heocagonal. — ^Four axes : three lateral — equal — lying in
one planef and inclined to each other 60°; the fourth is
principal, at right angles to the three lateral, of different
length; sometimes longer, sometimes shorter. This is the

• fMtx^as (Tnahros), great. + o^fios {orthos), richt or straight,

t (i^ax^ {brachus), Bhort. § »\ifn {dine), inclined.

II • {a)t without and «e^«s.

26 MlKERAtOOt.

only yariable element in the system. Professor Miller
refers hexagonal or ^'rhombohedral" crystals to a system of
three axes of equal length, and equally inclined to eadi other,
the actual inclination varying with different substances.
This mode is more conyenient for calculations in the higher
branches of crystallography^ but it does not so clearly re-
present to the non-mathematical student the relations of the
various forms to each other, so that on the whole the
ordinary mode of referring the forms to a isystem of four
axeS| is preferred on the present occasion*

CHAPTER rVT.
REPRESENTATION OF CRYSTAL FORMS.

28. Fignrefl of Crystals. — ^The most common mode of re-
presenting crystal forms on plane surfaces, is by what is
known as " isometiical" or "parallel" perspective. This does
not differ from ordinary perspective, except that the vanishing
points are supposed to be infinitely distant. In other words,
lines which are parallel are always drawn parallel and not
converging, and equal lines which make equal angles with
the plane qf projection (the paper), are made equal in length.

Fig. 19.— CuBiE IN Obdikaiiy Fig. 20.— Cttbe in Tajslai^xl

PEBSPECmVE. PEBSFECnVB.

The difference between parallel and ordinary perspective
is shown in figs. 19 and 20. In fig. 19 the cube is drawn in
ordinary perspective, and the parallel and equal lines cc,bb,
and a a, are seen to be converging ; and although they form
equal angles with the plane of projection, are drawn of
unequal lengths. In fig. 20 the cube is drawn in parallel
perspective, and the difference is very easy to be seen, for here
the lines a a, 6 6, cCy are evidently parallel and equal in length.

28

UINERALOGT.

Crystals are often drawn, as in fig. 21, as if transparent^
but in complex crystals the multiplicity of lines is very con-
f asing, and even in simple forms the advantage is not great,
SO that crystals are more generally drawn as if opaque.

24. Positions of Crystals. — Drawings of crystals differ
much according to the position in which the axes are placed
with reference to the plane of projection. Thus, in addition
to the representations of the cube given in figs. 16, 19, 20, 21,
the cube may be drawn as in fig. 22, with two axes parallel
to the plane of projection, when it appears as a simple square,
or with the three axes equally inclined, as in ^g, 23. This
latter figure is said to be in isometrical perspective,* because
aU equal lines are here drawn equal in length. Of these
different modes, that shown in fig. 16 is usually preferred
for crystals belonging to the cubical system, and this mode
will be hereafter adopted in the present work. This is a
projection on a plane parallel to one face of the cube, that
marked 010 by Miller, by parallel lines which are not per-
pendicular to that face.

A

/

1 ..._.

/

/

Kg. 21. Fig. 22. Kg. 2a

A somewhat similar projection is often adopted for crystals
belonging to the tetragonal or pyramidal system, and for
the rhombic or prismatic system ; the principal axis being
placed vertically and parallel to the plane of projection.
Another mode is to place the principal axis perpendicular to
the plane of projection or parallel to the plane 001 of Miller,
and O P of JN'aumcmn. The advantage of this mode is, that

* From tfts {isos), equal, and /*trf*9 [metron), a measure.

REPRESENTATION OF CRYSTAL TORMS.

29

it shows tlie equality of the two lateral axes in the tetragonal
ff^tem, and the ratios of the macro and brachy-diagonals in
ti^e rhombic system. By the
ordinary mode of representa-
tion the crystals belonging to
these two systems may readily
be confounded ; thus, the
tetragonal pyramid, fig. 24,
may easily be mistaken for
the rhombic pyramid, fig. 25,
or vice versa, Figs. 26 and
27 show the other mode of Kg. 24. Fig. 25.

projecting the same pyramids; and it will be seen that
the distinction between
the two systems is now
very plain. Both modes
have their advantages,
however, and both will
be occasionally adopted
hereafter. Fig. 26. Fig. 27.

Crystals belongiug to the oblique system are often drawn
so as to show as many planes as possible, without much re-
gard to position, but it is generally better to project them on
a plane parallel to the clino-diagonal and the principal axis,
or to the plane 010 Miller, [ ooPoo ] Nawmann, the principal
axis being placed vertically. This mode, which we have
usually adopted in the succeeding chapters, has the advantage
of showing the exact amount of inclination of the clino-
diagonal to the principal In the anorthic system the crystals
are projected on a plane at right angles to the planes 100,010,

of MiUer, or ooPoo ooPoo , of Ncmmann.

In the hexagonal system the plane of projection is either
parallel to the principal axis or parallel to the basal plane
111 Miller, O P Naummm,

25. Crystal Maps. — These are representations on plane
surfaces of the sphere of projection, upon which are shown
the poles of the several faces. The orthographic projection
of the sphere is sometimes used, but the stereographic pro-
jecticAi is preferred, because it has the advantage of represent-
ing all great circles of the spheres hj straight lines or arcs of

30

MINERALOGY.

circles. In the ortbograpbic projection the sphere is supposed
to be viewed with the eye placed opposite the centre, bat at an
infinite distance. In other words, it is projected upon a plane
by lines parallel and perpendicular to it, as in fig. 28a; the
result is that areas near the circumference of the projected
circle are represented on a much smaXler scale than those
near the centre, and consequently much distorted as to form.
Thus, in the figure 28a, the points a h e d on the semi-
circle are plainly equi-distant, but of their projections
a h' c d\ a' V and c d' are nearer together than V c\ In
the stereographic projection the lines converge to a point
opposite the centre, but at a distance from the plane of pro-
jection equal to the radius of the sphere, as in fig. 285. The
result is that the outside areas are represented on a larger
scale than those situated near the centre; thus, a V and c d^
are projected farther apart than V c'; but the distortion of
parts is on the whole less than with the former projection.

A«a

a'

h'

f

*^ ^^"

\

^ '

J

Pig. 28a. Fig. 286.

A good idea of the principle of ortJhographic projection may
be obtained by supposing a hollow hemisphere viewed through
a sheet of glass, from an infinite distance, so that lines com-
ing from the interior surface may meet the glass screen as
parallel lines. If a tracing of the various objects on the
surface of the sphere be made upon the glass, the result will
be an orthographic projection of the hemisphere.

If now, through a. similar screen, a hoUow hemisphere be
viewed, which touches the glass at its circumference, the eye
being placed at a distance from the glass equal to the radius
of l£e sphere, will now look into the hemisphere, and if
the objects be traced where they appear upon the screen, the
l^9ult will be a stereographic projection of the hemisphere.

IlEPBESENTATION OF CBYSTAL FORMS,

SI

Crystal maps so produced convey a good deal of infor-
maidon which can hardly be represent^ in the ordinary
perspectiye figures, and they greatly facilitate calculations in
the higher branches of crystallography.

26. Zone-circles. — ^These maps are of great service in illus-
trating the relative situations of the zone-circles, as is shown
in fig. 29, which is a representation of the principal zones
of the cubical system. The construction of the figure is
evident: o^ o^ O3, etc., are the poles of the octahedral faces ;
a J tfa a^ etc., those of the flEtces of the cube; and d^^ d^ d^, those
of the rhombic dodecahedron. The zones are represented
by the lines, and it will be seen that the planes a^, etc., are
common to no fewer than four zone-circles.

Fig. 29.

27. Sphere of Projection. — ^The situation of the poles on

the '' sphere of projection" may be realised by considering
the figure as an ordinary school globe. The points a^ and
a^ will then represent the north and south poles respectively,
and the circle a^ d^ a^ d^ a^ the equator. If the line joining
the poles be regarded as the meridian of Greenwich, d^ wiU
be longitude 45^ E., and d^ longitude 45*^ W. The points
d^ d^ da and d^ d^ d^y will be respectively in 45*^ N. latitude,
f^4 ^^ ^- V^^1^40r TfI ^^ P^^P^^^ 1^ ^ quite clear th^vt

N

32

MINERALOGY.

Kg. 30.— NlBT lOR

Octahedron.

the latitude and longitude of all normals (Art. 18) may be
readily laid down, and their relations at once determined by
meams of spherical trigonometry. The angles of the normals
once known, those formed by the various planes with each
other are the supplements of these angles.

28. Crystal Nets. — In the absence of ordinary models

the student will find much advant-
age in the construction of models of
cardboard, by means of what are
known as crystal nets,* For this
purpose the surface of the required
figure is drawn upon paper or card-
board, this is then folded into the
required form, and fastened with
glue. Fig. 30 is the net for an
octahedron, the axes of which are
Y in length; ^g. 31 is a, net for a
cube with axes of the same length.
In converting such nets into models, they should be ac-

curatelv drawn on cardboard.
The lines aaaa should then
be cut half-way through the
card, from one side (after
cutting out the figure ac-
curately), a' a' a' half through
from the opposite side. The
model may then be folded into
complete figure. A very in-
structive model may be con-
structed as follows : a net of
cardboard, like fig. 30, is
carefully cut out, folded, and
gummed, into a complete
octahedron; a cube of glass is
now prepared, the sides being
Fig. 31.— Net for CtJBB. made of J" squares of thin
glass. This is built up outside the octahedron, as in fig. 32.
This compound figure shows the situation of the primary

* A complete set of "nets" for the simple forms of crystals has
been prepared by Mr. J. B. Jordan, of the Mining Record Office.

:^

7

ni

■a-

L

a

•a-

it

-a-

\

/

BCfRESEirrATION OF CRYSTAL FORITS.

33

octahedron within the cube, and the situation of the axes in
bothfigures. Asimilarre-
presentation of the rhombic
dodecahedron within the
cube is given in fig. 33.

Occasionally sinular faces
of ciystaJs are indicated by
a similar mode of shading. Fig. 32. Fig. 33.

and this plan has been adopted by Mr. Kutley. A less
confusing mode is to indicate the faces by their proper
symbols^ or else by letters.

13—1 c

C3HAPTER V,

F0BM3 (ConfittNAl)— HOLOHEDRAL FORMS OF THE
CUBIOAL SYSTEM.

S9. Ik this system the axes are at i^ht anglee, and the
parameters equal. The several forma in this system are 13
in number, 7 being holohedral, having Uie general Erign hhl
in Millei'a system; 4 hemihedral, with inclined faces, having
the general sign xhkl, and 2 hemihedral, witli parallel faces,
with the general sign rhkl. In the present shapter the 7
holohedral forms vill be defined.

30, The Octahedron (Regular Octahedron, fig. 31).~
Symbol, 111 MiieheB and Miller; O X'aumarm, This is
the simplest form in the system, as the three parameters are
not multiplied or divided in any way, but ore met at normal
difltances from the centre of the crystal by a series of planes
which together compose 1^ complete form, the axes joining
the solid angles.

Fig. 34. Fig. 35. Fig. 36.

The regular octahedron is bounded by eight equal equi-
lateral triangles, the planes forming wit^ each ot^er angles
of 109° 28',* the normals therefore being inclined 70° SS*.
In fig. 36 the pr(^>er modifications of tlie general sign 111
* 109° 27' 3'; more eifwtly.

HOLOHEBBAL F0BH8 Of THE CUBICAL STSTEM. 35

ore placed over the indices of the four faces shown. The
complete symbol of the form will be 111. 111. 111. 111.

' 111. Ill 111. 111.

The face 111 corresponds with a plane catting the points
A.B.C, or a^ h^ 0^, or any other parallel plane in fig. 13.
Similarly, the face 111 corresponds with AC-B, or any
parallel plane ; and so on with the other faces.

Naumann's symbol is obtained by taking the initial letter
of the word octahedron to represent the primary form of the
system. The complete symbol might be written 000, to
harmonise better with the symbols of the other forms, but it
is always contracted to O. It should be observed that
Naumann's sign applies to the whole form, and affords no
means of distingui^ing between the several faces, unlike
Miller's more scientific system, which supplies a general
symbol capable of modification, so as to indicate every face
of the form separately.

We may also remark in this place, that the order of the
three indices of Miller's symbols never varies, the first
always refers to the axis A -A, the second to the axis
C-C, the third to the axis B-B, figs. 13, 14.

81. The Cube {Hexahedron, fig. 36). — Symbol, loo 00
Mitchell, 100 MiHeVy ooOoo Naumann, This form is
bounded by six equal squares, which consequently make
angles with each other, of 90°, and of course the normals do
also. Each face meets one parameter at its normal distance
(1) from the centre, and is parallel to the two others, or as
may be said, cuts them at an infinite distance, ie., not at all.
This fact is expressed by MtUer^s symbol, 100, as well as by
MitchelVa loo go , where the sign 00 stands for infinity, and
Naurnomn's ooOoo , where 00 stands for infinity, and O for
the parameter cut at its normal distance from the centre.
As already mentioned, Kallmann's symbol applies to the
whole form, so that the order of its several portions is quite
unimportant. It might indeed be written 00 ooO or Ooo 00 , as
the only fact to be expressed is, that the planes each cut one
parameter at the distance (1), and are parallel to the other
two. The symbol, however, is always used as written
above, ooOoo.

82. The Rhombio Dodecahedron; fig. 37. — Symbol,

So MISERALOOr.

lleo JHUchdl, 101 MiUer, ooOO JVaumann, contracted to
00 0. This form Is bounded by twelve equal rhombs, its
faces making angles with ea^Ii other of 120°, measured over
the edges, the nonnals being inclined 60°. The ratio of the
diagonals of the rhombs is as 1 : ^2 (I to the square root of
2). The axes join the opposite four-aided solid angles, and
each plane cuta two axes at the normal distance (1), and ia
parallel to the third.

The rhombic dodecahedron is the GraQatoicL of Haidinger,
and the Qranatoliedroil of Weita; it is a characteristic form
of garnet.

Fig. S7. Pig. 3ft Fig. 39.

33. The Three-faced Octahedron (tria^-oclahedron, fig.
38).— Symbols, 11m MUehell, hhk MiUer, mOO, contracted
to mO Ncmmamn. It is bonnded by twenty-four equal
isosceles triangles, and the axes j(nn the opposite eight-
aided solid angles. Each plane cuts two axes at equal
and normal distances (1) from the centre; but the third is
cut at a distance greater than (1), and less than (ao ). Ths
third parameter sometimes only a little exceeds, sometimes
very greatly exceeds the other two, consequently the angles
measured orer the edges, from face to face, and the nonnals
of these, are different for different crystallised substances;

The variable quantity more than (1), and lees than {« ),
is indicated by the letter m, so that the symbol of each face,
or of the complete form, is as already given, 11m. The
three-faced octahedron is like an octahedron upon which
three planes have been built up over each plane of the
original, hence the nama The thicker line around one
group i^ planes in the figure, shows the edges of the f^da-
mental octahedron. An infinite number of varieties tS this
form might exist, since m may be any ijuantity more than 1,

BOLOHEDRAL FORUS Of THE CUBICAL SVSTGU. 37

anil leas than infinity. In fact, however, only 7 different
values of m have been observed in natural crystals. The
limits of the form are evidently the octahedron, aa m becomes
smaller and fincLlly ec|uals 1, and the rhombic dodecahedron
as m becomes greater, and finally equals <x. The threo-
faoed octahedron was called Galenoid by Satdinger, because
it is a common form of galena. It also occurs frequently in
pyrites, and, with curved faces, in the diamond.

34. The Deltohedroil (twenty -/our faced tra/pexokedron
or ieonteVrahedron, fig. 39). — Symbols, Imm MitcheU, hkk
MUler, mOm Naumamn. Thie form is bounded by twenty-
four equal trapeziums or deltoids, and the axes join the
opposite four-sided solid angles. Each plane cuts one para-
met«r at normal distance (1), and the other two at distances
mm, greater than (1), but less than (go ), and equal to each
ot^er. Ab m approaches (1), the form approaches the
octahedron ; as m increases towards (oo ), it approximates to
the cube. These forms are therefore the limits of the delto-
bedron. Of course the angles of faces and normals vary with
different substances. It is the Lencitoid of Uaidinger, being
a characteristic form of leucite.* It also occurs frequently in

Fig. 40. Kg. «.

80. The Foor-facad Cnbe {Ut^aUs-hexahedron, fig. 40).
— Symbols, Iwtco MUchdl, hk o MiUer, coOm Navmann.
It is bounded by twenty-four equal isosceles triangles, and
tJie axes join 'Qie opposite four-sided solid angles. Each
plane cuts one parameter at normal distance, is parallel to a
second, and cuts the third at a variable distance (m) greater
than (1) and leas than (so ). The limits of tb% form are the
cube, when m equals oo , and the rhombic dodecahedron

* It will be seen in a later chapter that there are reanau for snp-
pounn that leucite U not a memoBr of Qie cubical syitem.

dd

lONBtUtOa?.

!

when it equals 1. Afi m is variable, the angles of faces ilnd
normals are different in the different varieties of forms.

The four-faced cube was called Flnoroid by ffaidinger^
tiecause of its ^quent occurrence in the minend fluor.

86. The Six -faced Octahedron (hexoJda-octaliedrm^ %
41). — Symbols, \nm Mitchell^ k It I Miller^ mOn Nomt
matm. This form is bounded by forty-eight equal and
similar scalene triangles, the axes join the opposite eight*
sided solid angles. Each plane cuts one parameter at its
normal distance (1), a second at a distance (m) greater than

1) and less than infinity, and a third (n) greater than
m) but still less than infinity. When n equals m the delto-
hedron results; when n becomes oo the four-£BU^ cube is
produced These two forms are therefore the limits of the
six-faced octahedron. It may be considered the most perfect
form of the cubical system^ as it contains all the possible
arrangements of + A + ^ +. ? taken three at a time. It is a
characteristic form of the diamond, and was for this reason
called Adamantoid by Eaidinger.

87. Poles of the Gubical System.— The projection of the

poles of the ''normals'^ to the
several faces of the cubical system
are given in fig. 42, which is an
octant of the sphere of projection
given in fig. 29 ; o is a pole of the
octahedron; a a are poles of cubical
faces; d d poles of the rhombio
dodecahedron. The poles ef the
three-&ced octahedron are variable
In situation, but fall onod; those
of the deltohedron on o (t, of the

four-faced cube on a d, and of the six-faxsed octahedron within
the triangles.

i^.4±

CHAPTER VL

FOEMS ((7on<mueci)~HEMTHEDRAL FORMS OF THE

CUBICAL SYSTEM.

88. The meaning of the term " hemihedral " has already
been explained {See Art. 20). The hemihedral forms of the
cubical system are six in number; four having inclined faces,
and two parallel faces. The hemihedral forms with inclined
faces are distinguished by the general symbol k h kl; those
with parallel faces by the general symbol whkL

89. The Tetrahedron, fia. 43. — Symbol, ^ MUcheU,
ff 111 MiUeTy ^ Ncmmomm^ This form is bounded by four
equal equilateral triangles^ which are inclined to each other
at angles of 70^ 32' (nearly)^ the normals being inclined
109'' 27' (nearly). Its faces correspond in situation and
relation to the axes, with four alternate faces of the octa-
hedron, consequently the sign is the same, but written with
the sign of division by two, thus, ^ to indicate their hemi-
hedral character. In Miller's system this is sufficiently in^
dicated by the sign ir. The axes join the central points of
opposite edges.

Fig. 43. Fig. 44. Fig. 4&

The tetrahedron may be very simply derived from th^
cube, as shown in figs. 44 and 45, where 45 is negative and
44 positive. If a crystal be simply a perfect tetrahedron, it

40 WITERALOar.

I ,

cannot properly be described oa either positive or negfttive ;
but occasionally faces of both the tetrahedrons occur in the
same crystal developed to a different extent In such cases
the negatiTe iaces are indicated by prefixing the negative
sign, thus, - ■^. Similar poBitive and negative forms exist
for the other hemihedral forms. It is evident that the
octahedron may be regarded as a combination of the positive
fmd negative tetrahedrons equally developed. The tetra-
hedron occurs in /ahlerx (hence called Tetrahedrite) and in
blende.

40. The Trigonal Dodecahedron (three -&ced tetra-
hedron), fig. 46.— Symbol, '-^ Mitckeit, e A A A Miller, ^
Naitmann. This form vhich is bounded by twelve eqtud
jsoceles trianglea is the hemihedral form of the deltohe(ton
(fig. 39) ; ita planes corresponding with alternate groups of
three faces of that figure. The axes join the central points of
the longer edges. T^e limits of the form are the tetmiedron,
when m equals 1, and the cube when m equals oo. It is a
form of frequent occurrence in blende aad/aklerz.

Eg. 40. Kg. 47. Kg. 48.

41. The Deltoid Dodecahedron (twelve-faced trapezo-
hedron), fig. 47.— Symbols, l^ Mitchell, ichhk Millar, "^
Nammcmn. This form is bounded by twelve equal deltoids
or trapezoids ; its fiices correspond with alternate groups of
faces of the tbre^-faced octahedron (fig. 38).'^ The axes join
the opposite fournBided solid angles. Its limits are the tetra-
hedron and the rhombic dodecahedron, as m approaches 1 or
00 . It occurs frequently in bUnde and/oAfcre.

43. The Biz-faoed Tetrahedron {hexakii mrahedron),
fig. 48. — Symbols, ~ MitckeU, k hkl Miiler, "^ Na/wmann.
This form is bounded by twenty-four equal scalene triangles,
which correspond with alternate groups of six of the six-

HEUmEDBAL FOBU8 OF THE CUBICAL STSTEH. 4l

faced octahedron (fig. 41). Its axes join the oppOBitfl four-
Hided Bolid angles. The limits of the form are iJie trigonal
dodecahedron and the deltoid dodecahedron. Good examples
occur sometimes in horaeile.

43. In the four hemLhedral forms juat described, no face
is parallel to any other face. They are often found in
natural crystals combined 'with some of the forma previously
described, but never 'with the two forms, with parallel faces,
now to he deecribed.

44. The Pentagxmal DodecahodTon, fig. 49.— Symbols,
!^ MileheS, rhko Miller, =?= Naumann. This form is
bounded by twelve equal pentagons, corresponding in situa-
tion 'with alternate planes of the four-faced cube. The axes
join the central points of the opposite longer edges. The
limits of the form are the rhombic dodocabedron and cube, as
m equals 1 or oo. It is sometimes called Fyritoid, becMisa
it is a characteristic form of iron pyrites and cobalt pyntes
(cobaltit«).

Ilg. 49. Tig. sa

46. The Trapesohedron (irregular twenty -four faced
trapezohedron), fig. 50. — Symbols, ['=?] Mitchell, rhkl Miller,
~ Naumann. This figure is bounded by twenty-four equal
trapeziums. The axes join the opposite equi-angular four-
sided solid angles. Like the wx-faced tetrahedron, fig. 48,
it is the hemihedral form of the six-faced octahedron, fig. 41;
but it is deri'ved according to a different law. In the former
the planes ^ correspond with alternate grmipt of the
planes \mn, in the latter 'with aUernate planes Imn. He
tlope* of the planes, however, correspond in both cases with
those of the siz-&ced octahedron ; to distinguish this figure
from the six-faced tetrahedron, fig. 46, &a agn is written in
bi'ackcts, thus, ['^^] Mitchell, or f^] Saumarm.

4S MlKSRALOGT.

The limits of form for the cubical system are as follows : —

a. The octahedron^ when m and n =s 1.

b. The cube, when m and n = oo.

c. The rhombic dodecahedron, when m = 1 and n = oo.

(f . The three-faced octahedron, when m = 1 and n is more
than 1 and less than oo.

«. The deltohedron, when m and n are equal, more than 1,
and less than od.

/. The pentagonal dodecahedron, when m is more than 1
and less than od, while n becomes oo.

CHAPTER VII.

tOEM {Con«nM(rf)-COMBINATIONS OF FOEMS IN THE
CCBICAL SYSTEM.

46. Of tbe tHiieen distinct forms of ciyatals described in
the precediiig cbapt«rs, the ploaea of several are ofben
combined in one ciyBtal, bo as to produce wliat are called
modified forma or comhtnatuma. Such modified forma are
indeed much more commonly met with in nature than are
the simple forms themselves.

In the figores illnstrating combinatione, the same letters
always indicate aimilat* planes, so that the student wilt have
little di£Sculty in tracing the relations of the Tarioua forms.

47. CouBiNiiTioKS or Fixed Holohbdrai. Fobhb with

K&CS OTHSB.

Fig. 61. Fig. 52. Pig. S3.

Octahedron and Cube, figs. 51 and 52. The planes o are
those of the octahedron, a those of the cube. It will be
seen that the slopes or inclvnatioTis of the corresponding
planes are alike in both fignres ; they have the same situation
with respect to the axes, and the same inclinations to each
other. The octahedral planes in fig. 61, however, are not
triangles bat irregular hexagons, nor are the cubical planes
square in fig. 62, as in the simple forms. !From thia we
Wm, thatf except in the simple forms, ^e shape of the plane

a UlHEBALOaT.

is quite unimportant, vhile its slope or inclination, as re-
ferred to the axes, is really its essential cliaracter.

The signs used to denote combinations are those of tho
simple forms which eater into the combination, placed one
after the other ; those of the larger planes first. The sign of
fig. 51 will therefore be 1.1.1, 1. os. oa ; that of fig. 52,
1. rx. CO, 1.1. 1 ; the cubical sign being in this second instance
placed first because the cubical faces are the largest.

Octahedron and Bhombio Dodecahedron, figs. 53 and 51,
the dodecahedral planes being indicated by the letter d. Tho
sign of the combination will be, for fig. S3, 1.1.1, 1.1. co;
for fig. 54, 1.1.0=, 111.

Kg. 54 Fig. 55. Fig. 66.

Cube and Bbombic Dodecahedron, fig. 55, 1. cc. os, I.I.go ;
5g. 56, 1.1. 00, 1. 00. 05.

Onbe, Octabedron, and Bhombio Dodeoahedron, fig. 57,
I. lc».

Rg. 68. Fig. 63.

48. coubinatioita of variable with fixed holohedrai.
Forms.

The combinationa above desciibed are combinations of
forms whose angles are fixed, the parameters being either 1
or 00, BO that no variable elements are introduced. We
have now to describe combinations in which the parameters
are sometimes variable, ni or n, so that a great variety of

COKBIKATIONS OF FOBMS IK THE CfUBICAL SYSTEM. 45

forms is possible aooording to (ihe values of those variables.
The illustrations given apply to modifications in which m or
n have medium values. The octahedral, cubical, and delto-
hedral planes are indicated as before by the letters o, a, and
d, respectively, n indicates the planes of the deltohedron, k
those of the ^ree-faced octahedron, 8 those of the siz-faoed
octahedron, and e those of the four-faced cube.

Octahedron and Deltohedron, figs. 58, 59, 60. In fig. 58
the octahedral planes are largely developed, so that the sign
-will be 111, Imm. In fig. 59 the deltohedral planes are
larger, and the sign will be reversed. Fig. 60 is a peculiar
form, having its planes about equally developed so as to pro-
duce a figure having a quite different aspect, with thirty-two
triangular faces. The triangles o are equilateral, the others
are usually isosceles. The sign may be written either way.
A figure of very similar general appearance, but fewer planes,
may result from a peculiar development of the octahedron and
pentagonal dodecahedron, as will be shown further on (fig. 78).

Octahedron and Three-faced Octahedron, fig. 61, 111,
11m; fig. 62, 11m, HI.

OotiAedron and Siz-faoed Octahedron, fig. 63, 111,
Imn; fig. 64, Imn, 111.

Octahedron and Four-faced Cube, fig. 65, 111, Imoo,
fig. 66, IfiiQo, 111.

Onbe and Deltohedroni fig. 67, loooo, Imm; fig. 68,

1991911^ loo 00 •

Cnbe and Three-faced Octahedron, fig. 69, loo oo , 11m ;
fig. 70, 11m, loooo.
Oube and Six-faced Octahedron, fig. 71, loooo, Imn;

fig. 72, Imn, loo oo •

Onbe and Fotur-fiGtced Onbe, fig. 73, loo oo , Imx ; fig."

74, Imoo , loo 00 .

Bhombic Dodecahedron and Deltohedron, fig. 75, lloo,

1mm; fig. 76, 1mm, lloo.

Bhombic Dodecahedron and Three-faced Octahedron,

fig. 77, lloo, 11m; fig. 78, 11m, lloo.

Bhombic Dodecahedron and Six-faced Octahedron, fig.

79, 118, Imn; fig. 80, Imn, lloo.

Bhombic Dodecahedron and Four-faced Cube, fig. 81,

lloo , Imx ; fig. 82, Imoo , lloo •

Hg. 6£ Kg. 61. Fig 6

Kg. 63. Fig. 64. Fig. 66.

Fig. 66. Fig. S7. Kg. 6

Hg. 69. Kg. 7ft Fig. 71.

COHBIKATIOM OF FOHUS IS TBB CUBICAL BTaiSU. 47

Vig-IS. ' I^ 73. Kg; 74.

Fig. 73. Fig, 76. Kg; 77.

Fig. 78. Fig. 79, Fig. 8ft.

Fig. 81. Fig. 82. Fig. 83.

48 UIHBBALOGT.

49. Oonyilex OomblnationB. — A. careful study of the fore-
going examplea will enable the student to read almost every
possible holohedral combination in this system with &oili^,
and it will be good practice for him if he will devise for
himself other combinations than are here given. An exr
ample of the very complicated forms which are sometimes
met with is given in fig. 83, vrhich represents one comer of a
crystal of fluor, &om Mr. Turner's collection. The crystal
had in all one hundred and fourteen faces. The signs <^ the
faces are as follows :

Actual measurement of
the faces enabled Levy to
assign the numerical values
to m and ti, given in the
third column. A still mole
complicated form is shown
in fig. 84, which representa
a cr^tal of floor &om Bee-
ralstone, in Devon, which
formed part of Mr. Phillips'
collection. This oiystol
if complete would have had
throe hundred and thirty-
eight foces. One comer
Fig. 84. o^y is drawn in the figure,

o = 111

d = Ilotf *<

cohbivationfl of fobhb of the cubical systev. 49

50. Combinations of Holohedbal with Hehihedral

Forms.
Octahedron and Pentagonal Dodecahedron, fig. 85,

111, '^; fig. 86, i^?, 111. In fig. 87 the two sets of
planes are about equally developed, and the result is a figure
bounded by eight equilateral tiiangles and twelve isosceles
triangles, and having the same sign as fig. 85. It has a
Bupei^cial resemblance to fig. 60, but has only twenty in-
stead of thirty-two planes.

Octahedron and Irregnlar Trapezohedron, fig. 88, 1.1.1
p=5];fig. 89,p??],lll.

Cube and Tetrahedron, fig. 90, loo oo , 'i.\ and fig.

91, »f, loo 00.

Cube and Three-faced Tetrahedron, fig. 92, loooo,
'^; fig. 93, ?2^, loo 00 . .

Cnbe and Deltoid Dodecahedron, ^g. 94, loooo, ^y»;
fig. 96, i^, loo 00 .

Cnbe and Six-fiEtced Tetrahedron, fig. 96, loooo,
fig. 97,255,10000.

Cnbe and Irregnlar Trapezohedron, fig. 98, loooo,

V?]; fig. 99, PfS], loooo.

Cnbe and Pentagonal Dodecahedron, fig. 100, loooo,
*-!=; fig. 101, !5?, loo 00 .
Bhombic Dodecahedron and Tetrahedron, figs. 102

and 103, lloo , ^ ; fig 104, ^\ - Hoo .
Bhombic Dodecahedron and Deltoid Dodecahedron, figs.

105 and 106, lloo,!:^; fig 107,-1 loo, lip.

Bhombic Dodecahedron and Three-faced Tetrahedron,

^g. 108, lloo, ??p;fig. 109, i!J?, lloo; fig 110, ^J!p, lloo.
In the last figure the value of m is greats than in the
other two, so producing a peculiarly-formed crystaL

Bhombic Dodecah&ron and Six-faced Tetrahedron,

fig 111, lloo, ?=?; fig. 112, i=?, lloo.

Bhombic Dodecahedron and Pentagonal Dodecahedron,

fig 113, lloo , i2= ; fig 114, 1^, lloo .

Bhombic Dodecahedron and IrrlBgnlar Trapezohedron,

fig. 116, lloo,[?25]; £g. 116, [?="], lloo.

13—1 D

Imn ,

UHEBALOGT.

Kg. 85. Pig. 80. " Fig. (

%. 88. :Kc. 89. x^ sa

np 91. rig. S3. Fig. S3:

Kg. 01 Fig. OS. Fig. sa

COHBINATKWS OF FOBUS IN THE COBICAL BtSTEU. 51

Fig. 109. Fift no. ^"B- "1*

Kg. 114 Fig. lis rij "».

Pie 115. Kg. 118. ^ '"■

Fig. 118. Fig. no- ^ ""•

OOMBINATIOKS OF rOaMB ID TBE CUBICAL BTStKU. . 53

SL COUBIKATIOHS OF HeHIBKDBAL FobUS WITH UCB
OTBZB.

Positive and NegatiTS Tetrahedroiu, fig. 117, ^,~i^.
When the poeitiTe and negative planes become equal, ths
reaalt ie an octahedron, wMoh may therefore be regarded as
a combination of the two tetrahedrons.

Tetnliedron with Three-faced Tetrahedron, fig. 116,
!!', !^ J fig. 119, '^, S; fig. 120, U-', - '-^; fig. 121, !=?, "■

fig 122, !^,-H.s + ■-;'.

Totrahedron with Deltoid Dodecahedron, fig. 123, '^
fig. 124, i^, ';J; fig. 125, ^,-'f.

Tetrahedron with Six-llBced Tetrahedron, fig. 126, ^

54 UINEHAIOaT.

63. A complex form occurring ia &Merz is given in fig.
128, where o = S!, 71 = '^, d=lloo.

A still more complex form
whicli ocoors in ^e same
mineral ia given in fig. 129.
The dgns are as follows :—

«»=-!;? =122
n =+15= =122
e = Imao =13=0

Fig. 129. d = llto

68. Platonic Bodies.— These are the only regtdar solids

which can be formed, ie., the only bodies which are bounded

by equai, almilar, regular, and rectilineal figures. They are

five in number, viz. : —

^e first three of these forms are common among natural
erystals, bnt the two latter have not been observal Figs.
49 and 87 sometimes afibrd a near t^proach to them, bat Uie
bounding planes are not tqnUateral pentagons and triangles,
respectively.

54. The series of figures of cubical forms and combina-
tions might be very much extended, but it will be found
abundantiy sufficient by every careful student. A few more
remarkable combinations will be given when the minerals in
which they occur come to be described.

CHAPTER VIIL

FORM (CofKinuecQ— TBDB TETRAGONAL OR PYRAMIDAL

SYSTEM.

55. Axes. — ^In tliis system there are tbree axes as in the
cubicaly and they are also placed at right angles to each
other, but thej are not equal in length, one being longer or
shorter than the other two. This is called the principal
axis, Hie two that are equal are lateral axes.

66. Angular Elements.— The angle made by the principal
axis with the normals (Art. 18) to the planes of one of the
chief pyramids (usually the square pyramid of the so-called
second order, figs. 133, 134), occurring in any natural
substance crystallising in this system, is called the cmguJar
element of that substa^ca

Thus, if c e, fig. 130, be the principal axis
and c a; a plane of the chief pyramid, then
n n^ will be a normal to that plane and the
angle n^ n e will be the a/ngtUar element.
With an angular element of 45*^ the planes
of the chief pyramid of the Jirst order m this
system would coincide with those of the regular
octahedron of the cubical system. This angle
has not actually been met with in nature, but
chalcopyrite has an angular element of 44^ 31',
so that some of its forms are scarcely dis- ^g* 130.
tinguishable from those belonging to the cubical system.
The principal pyramids of the minerals anatase, nagyagite,
and matlockite, are very acute, the angular elements being
about 60^ Very obtuse pyramids are met with in cas-
siterite, rutile, scapolite, and zircon, while the chief pyramid
in idocrase is so obtuse that its angular element is only 28° 9'.

66 UIVEBALOGT.

Witb ft few excepticma tbe perspective figures illnstrating tliia
cliapter are those of ciyatala with medium angaUr elements.
BV. Holohbdbal FOBIDI — Ptbakids. The only complete
holohedral forms in tlie pyramids A it 2 in which all ^ree
eigns are £nit«, i.e., leas iiian <c . They are of three orien,
as follows : —

Ist. TbeTatrBfTonalPyramid, of first order, fig& 131,132.
Mitchell, 111 01 hftl MUier, F. Naumann,
These are bounded by ^bt
equal iaotcdes triangles.
They are therefore octa-
hedrons, but difier from
the regular octahedrons,
I fig. 15, in which the planes
are equilateral triangles.
In fig. 131 the principal
I axis /- lis longer than the
I lateral axes h-h, h-h,
_ Fig. 132. In £g. 132 it is shorter.

The edges terminating at the principal axes are termed
polar, those which only connect the lateral axes are laUrat

1

Kg. 183. Fig. 134 Fig. 135.

2nd. The Tetra|>ini8l Pynunid, of second order, figs. 133,

J34.— Symbols, 1 oo 1 MUck^ 101 or hoi MiUer, Poo

Naumtmn. ^Diese do not at all difier in appearance from the

pyramids already described, but <mly in the situation of tho

THE TKTIUaOirAL OK VtKAMIDAL STBTEU, 57

lateral axes, aa shown in the figures. I^. 136 is a plan or end
view of thesa two ordeis of tetragonal pyramids, the completed
lines showing the eitnation of the lateral planes in the pyramid
of the firat order, the dotted lines those of the second order.

Fig. 136. Jig. 137.

3rd. The DitetragonalPyramidB, fig. 136.— Symbols, Iwil
MitehtU, hkl MiUer, m P n Nmtmarai. These pyramids aro
bounded by sixteen equal scalene triangles, "nie origin of
these pyramids will be understood &om a consideratioa of
fig. 137, which is a plan of the crystal ahowiog the lateral
axes h-hfk-k. It will be seen that each face would, if
produced, cut the prolonged parameters at pointe a; x beyond
h — h, k — k, Thia distance o x, which is always greater than
oh at oh, is denoted by the symbol m, consequently the
t^mbol of the form will be Iml, In the figure oa! = twic«
o h, conaequeutly m = 2, and the particular symbol of the form
will be 121. la these pyramids m may have any value
greater than 1 and less than as , as indicated in fig. 138,
which also shows the situation oS the axes in tetragonal
pytamids of the first and second orders. Here AAAA
are fkces of the pyramid of fiist order, symbol 111 ; BB,
etc., are faces of pyramids of the second order, symbol loo I ;
CO etc., faces of Uie ditetragonal pyramid, with the iiymbol
12^1; 00. are faces of other ditetragonal pyramids, with
tfie symbols 11^1, 121, 131, 141, respectively, aa in-
dicated by the dotted lines. From this figure it is evident
that the number of possible ditetragonal pyramids is infinito,
m having all possible values between 1 and co , the limits of
tiie pyramids <^ first order and second order. In the case
when the parameter t» is 2(, as shown in the fignro at 00

58 UiNEtULoaY.

etc., the angles at dd are nearly equal to tlie angles at h 1
or i 1, and the Buctoen bovmdmg planes of the form are
aeaiene, but scarcely differ from, isoaceiet triangles. In this
case the form maj' be mistaken for a combination of the
pyramida of Hie first and second order, with the symbol
111 + loo 1,

^::%:=.^-:

ing. vis.
08. DerivatiTe FrnmidB. — From each of the pyramids
described in Art. 67, othera are derived by increasing or
diminisfaing the principal axis, the lateral axes remaining
unaltered, as shown in fig. 139, which represents a series <^
three j^rr&mids of the firat order, all relating to the same
seriea t^ axes. The primary pyramid A is inclosed in
another more acute, a 2, in winch the principal axis is
doubled. It also incloses a more obtuse pyramid, a }, in
which the principal axis is reduced one-half. The symbol of
A is therefore III, that of a 3 is 112, that of a J, lU.

THG TETKAaONAt Oft fVOAUIDAL SYSTEU, 69

The general f^rmbol, expressmg the whole serieB, will tiifm-
{orehellmMUcheU, hhlMiuer, mP I^aumann. Similur
pjnramida may exist of the second order ,

with the general symbol 1 co m Mitchell,
hoi Miller, m F oo Naumann, all being
derived in a siinilar way. These are also
derived ditetragonal pyramids with the
geoeral Bymbol Imn.

B9. HoLOHEDRAL FORUS — pRiaus. TheBG
also are of three orders corresponding with
the pyramids already deBOibed : —
' 1st. Tetnjfonal Prism, of £rst order, fig.
140.— Symbols, llao, wool Jfticfei^ 110,
001 MiUia; oo P, P IfaKmaim. Thin "» *

prism is shown in the fignre in relatioa
to its corresponding pyramid, which is en-
closed by it. It is also represented by
the lines AA&A., in fig. 138.

2nd. Tetragonal Prism, of second order,
fig. 141.— Symbols, loo do, oo a-1 MilchtU,
100, 001 Miller, ooPoo, OP JVauwwntt.
This is shown in relation to its correspond-
ing pyramid in fig. 141, and to the pyramid
of first order in fig. 142. These prisnls of
first and second orders, like the correspond' I^g. 13%
ing pyramids, differ only in the sitoation of the latend axes.
In both, the principal axis joins the central points of the
top and bottom planes called the basal
planes or basal pinacoide. The poritions
of the lateral axes are clearly shown in
the diagrams. BBBB, fig. 138, indicate
the planes of the prism of second order.

3rd. The Sitetragonal Prism, fig. 142a.
—Symbols, Imoo , oo col Mitchell, hko,
001 Miller, eoVn, O'P ffaumann. This
prism, like the others, is shown in relation
to its corresponding pyramid. 'When n»
equals 2^, the base of the prism scarcely
dilSbrs mim a regular octagon, when the Fig- 140.
form may be mistaken for a combination of the sqiiai-c prismH

«0

llllteRi.LOGT.

at the first; and second order. Unlike the pyramids, -wMali are
complete in themselves, these prisms are open or ineom^te
forms, OS the length of the principal axis is in no w^y in-
dicated bj their symbols. The planes at top and bottom are
not inolnded in the " form," but have a separate symbol of
their own, viz. : a ool Mitchell, 001 Miller, or OP Xaumann.

Eg. 141. Fig. 142. V- Fig. U2a.

60. Order and Siokificance of Stubolb. — The student
must bear in mind that in this and the following systems the
three portions of each symbol, as 111 or loo 1, refer not only
to their corresponding parameters in regular order as ex-
plained in Art. 30, but they refer here, and in the systems
yet to be described, to parameters which are not equal to
each other as in the cubical system. Thus, the symbol 111
does not imply that the first, second, and third parameters
are equal, but that they are respectively undivided or not
multiplied. Inll|,forinstance, the ^ of the third parameter
may be greater, absolutely, than the 1 of the first or second
parameters : it simply implies that the face in question cuts
the third parameter at three-fourths of its own pi-oper length.
This fact must ever be borne in mind

<^>

CHAPTER IX.

FOBM {Continued) — THE TETRAGONAL SYSTEM—
HEMIHEDBAL AND TETARTOHEDBAL* FORMS.

61. From each of tlie forms just described, with the ex-
ception of the prisms of first and second orders, hemihedral
forms are produced hy the development of one-half the faces.

The hemihedral forms with inclined faces are ''sphenoids'' f
(irregular tetrahedrons), trapezohedrons and scalenohedrons ;
those with parallel faces are four-faced pyramids, differing
only in the situation of the axes from the holohedral
pyramids of first and second orders.

62. Hemihedral Forms of Tetragonal Pyramids.

In the following figures, 143 to 226, faces parallel to the
pyramids of the first order, llm = hhl = mV, are lettered (a).

Faces parallel to the pyramids of the second order, 1 oo m =
hol = Poo , are lettered (6).

Faces parallel to the ditetragonal pyramids, lmn = hkl=
m'Pn, are lettered (c).

Prisms of first order, lloo =110= ooP, are lettered (m).

Prisms of second order, loo oo = 100 = ooj?oo , are lettered (n).

Ditetragonal prisms, Imoo =hko= ooP n, are lettered (q).

The basal plane, oo ool = 00 1 = OP, is lettered (o).

(1.) Sphenoids deiived from pyramids of first order, fig.
143. Symbols, ^ or i^ MitcheU, | or !!^ I^cmmann, kIII
or ichhl MUler, The mode by which this sphenoid is
derived from the pyramid is shown in fig. 144, which repre-
sents the pyramid within the sphenoid. Fig. 145 shows its
derivation from the corresponding square prism. Fig. 146
shows the derivation of the corresponding negative sphenoid
-Khhl.

* rtra^nt (tetartos), fourth, and t^^a,
t sftvit (sphenoa), a wedge, and it^s.

62 MINEBALOGT.

(2) Sphenoids derived from pyramids of second order, fig.
147, symbols *-f-* or ^ MitcheU, I^ or 2f= Naumann, kHoI
Miller, Fig. 148 shows the mode by which it is derived
from the pyramid loo m, and fig. 149 its relation to the cor-
responding square prism loo oo . Fig. 160 is the negative
sphenoid -ichoL

68. Hemihedral Forms of the Ditetragonal Pyramid. —

These are of several kinds according to the special law of
development in question. In order to make liiese plain we
will represent the eight upper planes of the ditetragonal

pyramid, fig. 151,* the symbols $^62 e^ and the eight

lower planes by the symbols e\ e\ e g. The various

hemihedral forms will then be as fcnlows : —

(1.) The tetragonal scalenohedron, fig. 152. Symbols, ^
Mitchellf ^ NawmanUy Khkl MiUer. This is produced by
the development of the planes e^ e^^ e\ e 4, e^ e^^e^ e\. This is
the positive scalenohedron, by developing the I'emaming faces

instead of those mentioned, the negative form k A ^Z will result.

(2.) A very similar form, differing mainly in the situation
of the axes, is produced if the planes eg e^, e\ e\, e^ e^, e ^ e\
are developed. Mitchell and NaumanTCa symbols are the
same as for the preceding figure, but Miller distinguishes it
by ate sign Xhkl. The corresponding negative form iaXkhl,

(3.) l^e pyramidal trapezohedron, ^g, 153, is produced by
developing the faces e^ e^ e^ e^, c'g e\ e^ e'g. No special
symbols are given by MitcheU or ^aumann, but MiUer^s
is a hkl for the positive form and akhl for the negative.

The three forms just described are hemihedral with
inclined faces; a hemihedral form with parallel faces remains
to be described.

(4.) The hemihedral double four-faced pyramid, which
differs from the holohedral pyramids of first and second order
only in the situation of the axes, is produced by developing
the faces e^ 63 e^ e^, e\ e*^ e\ e\. MitcheU and Nammcmn have
no special symbols for these pyramids, but Miller*8 are irhkl
for the positive, and irk hi for the negative.

64. Tetartohedral Forms of the Ditetragonal Pyramid.

— ^The hemihedral double four-faced pyramids just described

* Only a few of the letters are put in, for the sake of clearness,
and for the same reason tiie principal axis is omitted.

^ THS TETBAQONAL 8TSTEM. 63

Pig. 143. Fig. 1«, Fig. 145. Rg. 146.

Fig. 147. Fig. 148. Fig. 149.

Fig. 151.
Fig. 163. Fig- 154.

64

MINERALOOT.

themselves admit of a hemihedral development, so producing
sphenoids of only one-fourth the original number of faces.
It* is however doubtful whether these sphenoids have been
observed in nature. They would differ from the sphenoids,
figs. 143, 147, only in the situation of the axes.

65. Hemihedral Forms of the Ditetragonal Prism. —

Symbol, ^. These will be square prisms differing from
those of the first and second orders only in the situation of
the axes. Fig. 135 shows the situation of the lateral axes in
the prism lloo and loo oo ; fig. 154 their situation in the
ditetragonal prism Imoo c^C2 Cg, and the positive hemi-
hedral square prism ^ i^ i^ Iq i^ produced by developing the
faces Ci Cj c^ <Sj, The negative prism - ^ is produced by
developing the remaining faces.

66. Sphere of Projection of the Tetragonal System.—

This is E^iown in
fig. 155, the con-
struction of which
is evident. The
centre (o) is the pole
of the oasal planes
00 ool. The poles
of the faces of the
*h pyramids of first
order llm, will fall
on the lines ox^, 00:2,
ofCg, ox^, more or
less distant from o
according to the
greater or less angu-
lar element of tiie
crystal in question,
Kg. 155. the"latitude"being

equal to the ^' angular element." The poles of the planes of
second order pyramids, loom, will fall on the lines oh^o^h,
ok, o-k in the same manner; those of the ditetragonal
pyramids, Inm, will fisdl in the triangles. The poles of the
prisms lloo will be at a^ o^g x^ x^ those of the prisms loo oo
at A, - A, A;, - A; ; those of the ditetragonal prisms Inoo on the
line h, x^, k, etc., and between the points marked.

CHAPTER X.

FOBM lConiinued)^KQiWI[EpnAL OOMBINATIOKS OF TH£

TETBAGONAL SYSTEM.

' 67. CombinationB of Pyramids with each other. — (1.)

Combinations of pyramids of the same order {derived
pyramids). These will be understood by a reference to fig.
156, which represents a combination of the three pyramids
like those shown in fig. 139. The faces of the primary
pyramid are in both figures indicated by the letter A, those
parallel to the acute pyramid by a^ ; parallel to the obttise
pyramid by a|,' Other combinations of pyramids of the
same order are also given in figs. 157, 158| in which A = the
pyramid 111, a the pyramid l}m.

(2.) Combinations of pyramids of different orders. Fig.
159 shows a combination of the pyramid of the first order
a {llm)y with the tetragonal pyramid of second order and
different slope loo m. In fig. 160, a is the pyramid 11m, e
the ditetragonal pyramid 1mm; fig. 161 is a combination of
the pyramids Inm (c) and 11m (a); fig. 162 is 11m (a) with
loo m (6), in which 6 is a pyramid of different altitude to a
{i,e.y m has different values in the two cases).

68 Pyramids with the Basal Plana— Figs. 163, 164,

show combinations of incomplete pyramids, with the basal
pinacoid o. The symbol of fig. 163 is }lm (a), oo oo 1 (o), of
fig. 164, Inm (e), oo oo 1 (o)r

69. Combinations of Pyramids with Prisms^— (K) Com-
binations of pyramids and prisms of the same order. Ex-
amples are given in figs. 165 and 166, where a is the
pyramid and m the prism. The figures represent combina-
tions of forms of the first order, but with a slight change
of position would equally represent those of the second order;
13—1 &

Kft 169. Fig. leO. Wis. 161.

Fig. 162. Fig. 165. Pig. 164.

COMBINATIONS OF THE TETRAGONAL SYSTEM, «7

' (2.) Combinations of ditetragonal pyramids and prisms are
given in figs. 167, 168, whei'e c is the pyramid and q the
prism.

(3.) Combinations of prisms of different orders. Fig. 169
is the prism of first order lloo (m) combined with the priam
of the second order Ico oo (w) ; fig. 170 is prism of first
order lloo (w), with ditetragonal prism Iwoo {q). Each
shows the basal plane oo ool (o).

Pigs. 171, 172 represent the pyramid of first order (a) with
prism of second order (»), the symbol being 111, loo oo .
. Fig. 173 is the pyramid of first order (a), with ditetragonal
prism {q)y having the symbol 111, Iwoo .

Fig. 174 is a ditetragonal pyramid (c) and ditetragonal
piism (q). The symbol is Iwm, Inao , as the h has different
values for pyramid and prism, it is in the latter distinguished
by an accent.

Fig. 175 is the ditetragonal pyramid (c) and square prism
of first order (m), with the symbol Inm, lloo .

Fig. 176 is the pyi^amid of first order (a), of second order
,(5), and prism of first order (m), the symbol being 111,
loo 1, lloo.

Fig. 177 shows the similar planes, except that 6 is loo m.

Fig. 178 shows the pyramid of first order (a), the dite-
tragonal pyramid (e), and the prism of second order (n), with
the sign 111, \nm, loo oo .

Fig. 179 is a more complex form, showing pyramid of first
order (a), of second order (6), prism of first order (tw), of
second order (w), and the ditetragonal prism (g), with the
basal plane (o). The symbol will be 111, loo 1, lloo , loo oo ,
Inoo , 00 ool.

Fig. 180 is still more complex, containing pyramid of first
order (a), two pyramids of second order (6) and (6'), dite-
tragonal pyramid (c), square prism of first order (m), and
second order (w), with ditetragonal prism {q), and basal
plane (o). The complete symbol is 111, lool, loom, Inm^
lloo , loo 00 , Inoo , 00 ool.

Fig. 181 shows pyramid of first order (a), two pyramids
of second order (5) and (5'), ditetragonal pyramid (c), prism
^f first order (m) of second order (n), ditetragonal prism q.
Symbol 111, loo 1, Iw m, \nm, lloo , loo oo , Inoo .

HIITEBALOOY.

Fig. 173. ^S- "^■

Fit 17lt Fig. lie. Fig. 177.

coubiHAibOKa of iHE iti&koosxL aatBtlOi.

Fig. 178. Fig. 179. Tig. 18ft

Fig. 182. Fig. 183.

Pig. 184. ^'e- 187. Fig- ]

UtNEEALOar.

Fig. 169. Fig. 190. Fig. 191. Fig. 192.

Fi£. 19a Fig. 194. Fig. 195. Fig. ]

Fig. 197. Fig. 198. Fig. 199. Fig. 2

Kg. 201. Fig. 202. Fig. 201 Fig. 20i

Fig. 205. Fig. 206. Fig. 207. Fig. 208. .

COMBINATIONS OF THE TETRAGONAL SYSTEM. 71

Pig. 182 shows three pyramids of first order (a) (a') (oT),
p;^mid of second order (6), prism of second order n, the
symbol is 111, llm, llm\ loo m, loo 1.

Fig. 183 shows pyramid of first order (a), ditetragonal
pyramid (c), prism of first order (m), of second order (n), with
the symbol 111, Inm, lloo , loo oo .

Fig. 184 is a very complex crystal of idocrase, described
by Mohr, having the following faces :

a = 111 6 irlool €"=144 m=ll<» g'=13oo

a' =112 c =122 c^'=124 n =1<»«> osooool

a^s 114 c'=133 c'"'=13t q =12oo

70. Vertical Projection. — ^A very convenient mode of
representing the planes occurring in minerals belonging to
this system is the vertical projection often adopted by
Professor Miller — a projection by lines parallel to the
principal axis on a plane perpendicular to that axis. A
seiies of holohedral figures drawn in this manner is given
from figs. 185 to fig. 208.

It will be observed that this mode of representing crystals
does not indicate the relative size or development of the
planes of prisms. The existence of planes of the prisms
dan indeed only bid indicated at all by the signs, placed
around the figure, as in fig. 186; where, if the sign n did
not appear we should conclude that the crystal represented
was a pyramid only, without the prismatic planes. * }

In figs. 185 to 192 similar planes are lettered, the rest are
left aS exercises for the student.

Up to fig. 195 the basal plane on ool (o) does not appear;
after that all the figures to 208 show that plane.

CHAPTER XL

rORM (CaiKittttccO—HEMIHEDRAL COMBINATIONS
OF THE TETRAGONAL SYSTEM.

7L Combinations of Hemihedral Forms with each other.

' (1.) The pbsitiye sphenoid ^ (a) with the negative sphenoid
- ^ (a'), fig.' 209. ^The student will note how much this
figure resembles the combination, fig. 117, in the cubical
system. Where the ''angular element*' of the tetragonal
crystal' in question approaches 45°, as in chaloopyrite ; it is
indeed impossible to distinguish the two forms without care-
ful measurement. Fig. 210 is the same combinationi but
here the negative sphenoid is the most developed

(2.) The positive sphenoid ^ (a), negative sphenoid - ^ (a),

and scalenohedron^* (e), fig. 211. .

, 72. Combinations of Hemihedral with Holohedral Forms.

(1.) Positive sphenoid ^ (a)/ with' the prism; of first order
11 00 (m). .This is lessJike fig.' 209 than it appears here.
(2.) Positive sphenoid ^ (a) and prism of second order

loo 00 (n); fig.- 213.' '

(3.) Positive sphenoid ^ (a') with double four-faced pyra-
mid loo 1 (6) fig. 214.

(4.) Pyramid of second order loo 1 (b) and negative sphenoid
• !52(a'>,fig. 215.

(5.) Pyramid of second order loo 1 (h) and scalenohedron
'J^ (e), fig. 216.

(6.) Positive sphenoid ^ (a), negative sphenoid - ?p (a),
scalenohedron *^ (e), and prism of first order 1 1 oo (m) fig. 2 1 7.

(7.) Positive sphenoid ^ (a), negative sphenoid - *" (a'),
basal plane a> ool (o), scalenohedrons ^ U\ and ^ (e),
fig. 218.

COUBIHATIONB Of THE TETRAOOKAL fiTSTEU.

Fig. 210.

COMfilKATlOKS 0» THfi TBTfiAGOKAL 8VSTSM. 75

(8.) Fositiye sphenoid ^ (a), negativo sphenoid - ^ (a'),
ecalenohedron ^ (e), derived pyramid of second order loo 2
(b), and prism of first order lloo (m), fig. 219.

(9.) Fositiye sphenoid ^ (a), negative sphenoid - ^ (a'),
positive sphenoid *^ (a% positive sphenoid 2^ (a'), basal
plane odooI (o), and five scalenohedrons ^ (e^^d^e^e*),
fig. 220.

78. A few vertical projections of hemihedral forms are
given in figs. 221 to 226.

Fig. 221 shows the planes of the pyramid of first order
(a), those of the hemihedral form of the ditetrag(Aial
prism 2p are indicated by the sign (g).

Fig. 222 is the hemihedral form of the ditetragonal prism
^ {q)y the hemidedral doable fotuvfaced pyramid ^^ = ahkl

(e), the pyramid of second order loo m (5), and ike basal
plane od ool (o).

Fig. 223 is the sphenoid derived from the prism of second
order !=:5 = «e 7*0^(6).

Fig. 224 shows the positive sphenoid derived from the
pyramid of first order ^ (a), the negative sphenoid (a'),

pyramid of second order (h) and (6% basal plane (o), the prism
of second order loo oo (n), and iJie ditetragonal prism (q).

Fig. 225 shows two pyramids of first order a and a\
ditetragonal pyramid c, sphenoid derived from a ditetragonal
pyramid c\ and the pyramid of second order (6).

Fig. 226 is a pyramid of second order (5), and three
sphenoids derived from ditetragonal pyramids cce»

1«M»

CHAPTER XII.

74. Axes and Elements. — In tliis ayBtem there are three
axes BitOBted at right angles to each otlier. Two of these
are known as IcUeral, the third is prineipaL Ail three are
of difieient lengths. The greater lateral or " macrodiagonal "
axis may bo generally indicated by the sign ± A, the lesser
lateral by the sigu±^, the principal by±t In giving the
symbols for the various forms and faces this order will always
be observed. A plan of the two lateral axes is given in fig.
227. The vertical axis is at right angles to these. The
system is.kn,own as rhombic, because its most perfect form is
a double pyramid on a rhombic base; as prinaatte, because
of the great number of prisms which occur in it.

Fig. 227. Fig. 228. I^. 229.

76. HolohedTal FormB. — The only complete holohedral
form is the rhombic pyramid hJd, in which h, k, I, are all
finite. This is bounded by eight triangular planes, each
cutting the three axes at some point less &an cc . lUiombic
pyramids with Hie ugn hkl are illustrated in figs. 228 and
229. From this complete form a series of pf^tial forms
result, when either h,k,Qtl becomes infinite; All of these
forms are bcomplete, iA, they most be combined with other

DEBITED RHOMBIC PTBAMIDSL 73

fonns to produce complete crystals* These jMurtiat forms,
six in number, are produced as follows: —

1» When h becomes infinite the " macrodome '^ ookl or odI 1.

2. When k becomes infinite the " brachydome*'Aoo ^ or loo 1.

3. When / becomes infinite the '< rhombic prism" Iikx^

orlloo.

4. When h and A; become infinite the ^' basal pinacoid " oo oo2

or 00 ool.

5. When h and { become infinite the ^'macropinacoid " odA^qo
or ooloo .

6. When k and I become infinite the *' brachjpinacoid "
Aoo 00 or loo 00 .

The forms lloo , hloo , and l^oo , when combined with
00 ooly compose n series of complete rhombic prisms, which
may be called prisms of the 1st, 2nd, and 3rd orders.

The forms ookl and loo oo together compose a rhombic prism
of 4th order.

The forms h oofand ooloo together compose a rhombic prism
of 5th order.

The forms oo ool, ooloo , and loo oo together compose a
rectangular prism.

76. Bight Bhombic Pyramids. — ^These are bounded by
eight equal scalene triangles* The general aspect varies
much according to the relative length of the axes. Fig. 228
represents a pyramid in which the vertical axis is much
greater than the two laterals; fig. 229, one in which it is
much shorter. The symbols of these pyramids will be 111
MitcheU and MUler, P Namrnaim,*

77. Derived Rhombic Pyramids.— Of these there are five
varieties as follows : —

a. With the parameter 7, multiplied or divided, conse-
quently the sign is lli7» MitcheU, III Miller^ mP Naumann.
h. With the parameter k, multiplied or divided, the sign

is 1ml MitcheU, \k\ Miller, rn Naumcmn.
c. With the parameter h, multiplied or divided, the sign

is mil MitcheU, All Miller, P7» Naumann*

* It must be remembered that as in the pyramidal system so here
the sisn 111 does not implv equaUty of the axes or parameters, since
each nas its own proper length; but simply tiiat they are neither
multiplied nor divideain the case in question..

78

UINERALOOT.

d. With the parameters k and I, multiplied or divided—
sigD. Inm MiteheU, Ikl Miller, mPn Ifawnann.

e. With the parameters h and I multiplied or divided —
Mgn m\n Miichdl, h\l Miller, mVn Naumann.

Of these the second and fourth are called " brachypyramids,"
the third and fifth " macropyramids."

76. Bie:ht Rhombic Prisms. — These ai-e incomplete forms
combined with the baeal pinaooid oo osl. They are of five
orders as follows: — The plane ooool MileheH, 001 Miller,
OF S'auTnann, oocnra in all —

1st Order — sign Hx Mitchell, 110 MiUer,aiB Nmanann.

2nd Order — fo^ m\'a Mitchell, h\^ MiUer,i»P NoMmann.
^ese are ualled " macropriBms."

3rd Order— Bign Imso MiUheU, ItO Miller, o=¥ Naumann,
Thepe are called " brachypriams."

/

^.-,

, Fig. 232. Fig. 231.

The relation of the prism Iloo to the axes is shown in fig.
230, whore »w» me the faces llw . The situation of the
prism within the i^ramidlU is given in %. 232. F%. 231
shows the rations of the three forms llos, i»l<x>, and
l)n«> , to me lateral, axes.

PYRAMIDS WITH DOMES AND PRISMS. 79

f 4th Order, the " macrodome" — ^gucxmim Mitchell, Okl
^ Miller, Poo Nautrmnn, combined with the " brachypinacoid,"

loo CO Mitchell, 100 Miller, ooPoo Naumann,

The position of this form within the pyramid 111 is ^ven
in figs. 233 and 234, where w represents the faces ooll.

5th Order, the "brachydome" — ^sign moom Mitchell, hOl

Miller, Poo Nwwmann, combined with the " macropinacoid "

00 loo Mitchetl, 010 Miller, ooPoo Nawnmnn,

Its position within the pyramid 111 is shown in fig. 235,
where v represents the face loo 1.

79. Bight Bectangular Pyramids. — ^These are sometimes
{)roduced by a combination of the planes of the macrodome
ooll (yo) with the brachydome loo l(i?) as in fag, 236. The
situation of the axes is well shown in the figure.

80. Bight Bectangular Prisms. — ^This is composed of the

bhree forms ooPoo , ooPoo , OP Naumann, these three forms

being the macropinacoid, the brachypinacoid, and the basal-

pinacoid respectively. This form is illustrated in figs. 237,

238.

. 81. Combination of Pyramids with Pyramids.—Pyra-

mids 111 (e) llwi (e'), fig. 239.

82. Pyramids with Pinacoids and Prisms. — Pyramid

111 (e) and basal pinacoid oo ool (c), fig. 240.

Pyramid 111 («) and macropinacoid ooloo (6), fig. 241.

Pyramid 111 (e) and brachypinacoid loo 1 (a), fig. 242.

Pyramid (e) with brachypinacoids and macropinacoids (a)
and (6), fag. 243.

The same with basal pinacoid: oo ool (c), fig. .244.^ -

Pyramid 111 (e) with prism lloo (m), fig. 245.

83. Pyramids with Brachydomes and Macrodomes.T-

Pyramid 111 (e) and the brachydome loo 1 (v), fig. 246.

Pyramid \nm (e), brachydome oolm (d), macrodome
obIw*' (/), and brachydome ooml («"), fig. 247.

84. Pyramids with Domes and Prisms. — Pyramid 111 (e),
macrodome ooll (t^?), and brachyprism 12oo (jp), fig. 248.

Pyramid 111 (e), brachyprism 12oo(^), prism lloo (w),
brachydome loo 1 (t?), fig. 249.

- Pyramid llwi (e% brachydome loow (v), brachyprism
Inoo fp'), and macroprism wloo (w), fig. 250.

HlKEnALOOT.

I

fig. !i33. Fig. 234, Fig. 235.

JTitf; 230. S^ 337. Fig. 238

Fig. 24a Fig. 2

Fig, 24Z. %. 241 Kg. S«.

BnOlimC C01CBIN1TI0H8.

8'3 HDTEBALOOT.

85. Domes, FriBms, and PisacoidB. — Ma^rodome colj («)i
brach^ptism 13<o (;>), and macropmscoid oolco (b), fig. 251.

Btachydome Icom (v), broohypinacoid looco (a), and
rhombic prignx lloo (m), fig. 252.

Braobydome loo m {v), and bracbyprism 12oo (p), fig. 253.

Mocrodome eoI2 (s), bracbydome Ico I (v), and basal
pmacoid oo a>l (c), figs. 254, 255.

Maorodome(»12 (mj), prism ll«:(fn), and basal pinacoid

00 ool (c), fig. 256.

Prism lloo(m), macroprism «loo (n), braohydome la>m
(u), and basal pinacoid an cnl (c), fig. 257.

Macroprism nlao(n), bracbypinacoid la)co(a), pyramid

1 11 (e), and baaal pinacoid oo ool (c), fig. 258.

A complex crystal of barytes, described by Dana, from
Cheshire, Connecticut, is illustrated in fig. 259. It eshibita
the following fonos : —

e =PjTWiad

ni

1«V

^ - ,.

lU

b = Macropinacoid

(C =

111

a>n

e" = „

111

oil

St = Prum

lloo

to" =

c = Basal pinacoid

(sgsl

vf = - „

1*«

«/"=

lT>\

n' = Macroprimn

21oo

The complete crystal contains no fewer than 80 planes.

Jig. 257. ■ Fig. 258. rig. 259,

TEBTICAL PBOJECTlOlfB 07 RHOUBIC CBTCTAL8. 83

86. Vertical Prujeotionfl. — A large Beriea of rhomHo
"crystaa projected oa a plane parfdlel to the baaal plane
00 ool by lines parallel to the principal axis is given in figa,
260 to 349; the Btudent will have Uttle difficulty in assign-
ing their proper namea to the various planea.

%. 260 is the pyramid 111 or 11m, 261 to 264 are
various combinations of pyromida and prisma, and 265 is
the pyramid with the basal pinacoid.

Kg. 269. Fig. 2S4. Fig. 265,

Figs. 266 to 271 are combinations of varioua prisms with
the basal pinaooid.

Rgs. 273 to 275 are varioua macrodomeB; 276 is the
macFodome with the basal pinacoid.

Figa. 277 to 283 are\ariouB brachydomee; 283 and 284
are braobydomeB vdih the basal pinacoid.

Fig. 286 is that particular combination of the brachydome
and macrodome which forms a double pyramid with rect-
angular base.

Fig. 286 is the macrodome and brachydome, the former
predominating.

Fig. 287 is the same combination with the brachydome
predominating.

Fig. 288 is another combination of domes, and figs. 239
-and 290 show various brachydomea and macrodomes with
the basal pinacoid.

Knra&iLoaY.

Kg. 266. Fig. 267.

Pig. 270. Rg. 271. Pig. 272. Tig. 273.

Pig. 274. Fig 275. Pig. 276. Fig. 277.

II II

Fig. 278. — Pig. 379. Fig. 28a 'itt- Fig. 281.

11 II

Fig. 283. Fig. 283. Fig. 284. Fig. S

BHOUBIC COUfitKATIOHS. 85

FSg. 286. Hg. 287. Fig. 28a

Kg. 28S. Fig, 290. Fig. 291.

II I! II

Fig. 293. Fig. 23t I

II II II

Fig. 296. Fig. 297. - Fig. 298. Fig. 299.

I

Fig. 300. i'ig. 301. Fig. 302. Fig, 303.

Fig. 292. Fig 293. Fig. 29t Fig. 295.

U1N£R1L0QT.

Fig. 304. rig. 305. Kg. 300. Fig. 3

*1-

II

Fig. 30P. Fig. 300. Fig. 310. , Fig. 311.

Fig. 312. Fig. 313. Fig. 314. Fif. 315.

II II

Fig. 316. Fig. 317 Fig. 31». fx^. 3ia.

ttHOSlBIC C01[llISA,TlOsa.

8d ItlKfiftALOOt.

Figs. 291 to 296 are combinations of various pyramids
and macrodomes.

Figs. 297 and 298, the same, "with the addition of the
basal pinacoid.

Figs. 299 to 314 are pjrramids and brachydomes, 315 to
328 the same, with the basal pinacoid.

Figs. 329 to 334 are pyramids, macrodomes, and brachy-
domes; in 335 to 349 the basal pinacoid is added.
* Many of the above combinations include also prisms^
macroprisms, and brachyprisms, but these planes cannot •
be shown by this mode of projection without lettering, as
explained in Art. 70.

87. Hemihedral Forms. — ^These are of three kinds, viz. —
a. Forms with inclined faces (icMZ). . .

. /3. Forms with symmetrical faces (c/<^^.
y. Forms with parallel faces (irhkl).
' They consist of sphenoids, hemipyramids; and prisms.

88. Bhdmbic Sphenoids. — ^These are derived from the
rhombic pyramids 111, £gs. 228, 229, by a development of one-
half the faces taken alternately. The relation of the positive
sphenoid to the axes is shown in fig. 350, the sign of which
is Y MitcJieU, iclll Miller, | Naumann, The negative

sphenoid 351 has the signs -^ ^i^heU, xlll MUter,-^

Naumamn.

' Corresponding sphenoids may be obtained from every

derived pyramid of each of the five orders described in

Art 75.

89. Hemipyramids. — ^A development of the group of four
faces forming any solid angle of the rhombic pyramid 111,
figs. 228, 229, produces a ciymmetrical form to which the sign
ihkl is given by Miller. The particulai* group of faces so de-
veloped is best indicated by Mitchell and Miller's symbols,
whichr assign a particular modification of' the general sign to
each plane.

For the group of faces around the angle k, fig. 228, the
full sign will be--^

111, 111, iiV 111; OT jua, hkl hkl m,

in which the central member of the symbol of each face pre-
serves its sign ( + or - ) unchanged. The symbol here will

BHOUSIC COUBIHATIONS. 6!)

"be ef*iil. In like manner for the group of faces around tbe
angle / the full sign vrill be —

111, 111, in. 111; or hki, m, hii, m,

in which the last member of the symbol of each face pre-
serves its sign unchanged. The symbol here may be ikkl.

Similar modifications of the general symbol may readily
be arranged for the faces meeting at each solid angle. Each
of the derived pyramids described in Art. 75 is subject to
similar hemihedral modifications.

90. Hemiliedral PriBms.— These are foi-ms consisting of
any two paira of parallel faces of the pyramids 111 or kid,
fig, 228, They have the general symbol irlll or 'ttlJd,
modified, as explained in Axt. 87, Prisms are similarly
produced from each of the brachydomea and macrodomes.

II II II

DO

MtHERALOat.

A combination of tiie positive and n^ativo hemiliedral
developments of the pvramid fiM is given in fig. 3S2, where
the large faces (e) belong to the form v/tkl, and the small ones
(i) to ikkl.

Fig. 359.

Fig. a

fig. 301.

Fig. 30i.

91. Vertical PrujeotionB of Hemiliedral Porms.— These
are given in figa. 363 to 362.

In the foregoing figures the following lettering is adopted.
Planes parallel to —

100= a

0=12 =012

010=6

colm =01m

001^0

oolin'=01m'

110= m

laam^doi

111^ e

nl« =n

101= V

l«2-/or

011=10

212 rzy-

150= p

113=!;

the podtion of the

8PHEBK or PBOJUCTIOK.

S3, fipben ofPn^eotion.— In fig-
chief poles of ihia
Byatem are indicated
on the sphere of pro-
jectbn. Theexam{de
chosen is the crystal
of batTtes given in
%. 364. The outline
of the prism llao (m) i
is indicated by a thick "*'
broken line. The
poles of the various
faces are indicated by
dote, and lettered to
correspond with the

% aei.

To draw the figure
a circle is drawn witli Fig. 363.

the centre c and any convenient radius c a, then the ax-iul
lines a~a, b — b, at right angles to each other.

The points mtm are Uien taken on the circumference of
the drole, the angolar distance am being 50° 60', and the
lines m m are drawn through the centre c. These points m
are tabe poles of the planes (llm ) m, fig. 36i.

By ^wing the dotted lines ax at _
rixht angles to cm, we get a projection
of the prism Ileo, iJie relatire lengths of
the latranl axes of which are as ca to cic ^
1-227:1.

The poles of V v are determined by meo*
suringinthearca-ftST" 18' towards -6,
as at $, and letting fidl the perpendicular %. 364

V on ac. The point « on the other side may be measured
directly from c.

For the poles of the macrodomes v^, to', and ui, the points
/^y, and S, are taken in the arc - a - 6 by measuring 28° 14',
38*^ 63*, aiul 68° 10' respectively, perpendiculars are then
dropped aa before.

For the poles of the planes « e, a point ( is taken in the
same wayon the arom ffa towards a, making m • = S5°43', and

93 mirsRAiiOOT.

dropping the perpendicular te; ^ is determined in the same
way, only making i| s= 55° 17'.

The remaining poles of the plane y are found by measur*
ing on the arc hev from h towards y 63° 58'.

The poles of all prisms will be on the circumference of the
circle ; of all brachydomes on (m; of all macrodomes on hh;
of all pyramids 11m on cm; of all brachyprisms on the arcs
am; of all macroprisms on the arcs hm; of all bracby-
pyramids on the triangles a c m; and of macropyramids on
the triangles hem.

CHAPTER XIIL
FORM (Conlinited)—TBE OBLIQUE SYSTEM.

93. Axn, etc. — "Has Bjebaa is bo called beoanse Its forms
maybe derived from an oblique octahedron or an oblique
prism. It has also been called monoeliriohedric, hemiprittnatie,
hemiorthotype, dirwrhombic, hemihedrie rhomiic, two and one
meTitbered, etc Tbere are three axes, Wo of which are at
right angles to each other, the third inclined at difierent
angles in difiWent minerals. The lengths may be, and
uBuallf are, all different One of the two axes which are at
right angles is taken for the principal, the other is called
orihodiagonal, while that which is inclined to the principal
is termed the ^nodiagonai.

94^ ElementB, — The rtuiabte conditions in this system
are, the ratios of two axes to the third, and the inclinatioD
of the clinodiagonal to the prindpal. These conditions will
be all defined if the following three angles, or their normals,
be determined, viz., the angles made respectively by the
planes loo 1 with loo so ,
Isol with ooool; and
lllwith osloo ;{or,aBiug
Nauraann's ff^i^bols, Pco
with cjoPoo ;Poo with OP;
and P with [oo Poo ]). The
normals to these angles
{". /3, y, respectively),
are die anguiar elemenia
of the minerals in qnes- ""S' ""■

tion, and a + gives the inclination of the clinodiagonal to
the principal axis.

95. Obliqae PyramidB. — The oblique rhombic octahedron,
fig. 365, is bonnded by eight scalene triangles in two seta
of four, viz., four equal smaller triangles, and as many equal
larger triangles. The four planes hM, hi^ hJd, hkl, compose
the form hkl Miller and F ^aumann. This is called the

"^'^

04 MINERALOGY

poeitive hemipjrranud. The four planes hid, hkl, hkl, hM,

compose the form IM Miller, - P Naumcmn, This is called
the negative hemipyramid. Together, these two sets of planes
compose the obliqye rhombic pyramid, which is therefore a
compound of two forms. The primary pyramid is, of course,

that whose sign is 111 or 111.

96. Derived Pyramids. — From the pyramids just described
a series of derived pyramids may be derived, shoilar in posi-
tion, but differing in magnitude. These may be conveniently
arranged in three classes, viz.: —

1st Class. — By multiplying the principal axis by any
number 911, greater or less than unity, a series of new positive
and negative hemipyramids are obtained, the symbols of

which are 11m and llm Mitchdl, mB and — mP Na/umarm,

2nd Class. — By multiplying the principal axis by ai\y

number m, and the orthodiagonal by 'any number n, we

obtain a second series of positive and negative hemipyramids,

the symbols of which are \nm and \nm Mitchell; mPn and

- mVn Naumann,

3rd Class. — Multiplying the principal axis by any number
m, and the clinodiagonal by any number n, we obtain a
third series of positive and negative hemipyramids, the
symbols of which are n\m and n\m Mitchdl; (mPn) and

— ^Pw) Naumann.

97. Open Forms. — ^These result when either A, h, or I, or
any two of them become zero. Some have two planes, some
have four, but of themselves they cannot form a complete
figura A large number of oblique prisms are produced
by their combinations with each other, some of which have
rhombic and some rectangular bases.

98. Oblique Rhombic Prisms.— These are of several kinds,
as follows: —

1st Order. — ^This includes two distinct ''forms," viz., the
form \\a:> MitcJidly 110 Miller, ooP Naumann^ having four
faces, and the basal pinacoid 00 odI, 001, or OP, having two
faces. From this prism two classes of derived prisms may
be obtained, simOar in position, but differing in dimensions;
the first class by multiplying the orthodiagonal axis by any
number greater or less than unity, producing the prism

OBLIQUE PRISMS. 95

Imoo , 00 ool; and the second class by similarly multiplying
the clinodiagonal, producing the prism mloo , oo ool.

2nd Order. — ^These are combinations of the four planes of
the clinodome ooll Mitchell, Oil MiUer, (Poo) Naumann^
with the orthopinacoid loo oo MitcheU, 100 Miller, ooPoo
^aumann.

From this prism a new series may be derived by mnl^-
plying the principal axis by any number more or less than
unity, producing the prism oolm, loo oo .

99. The Oblique Rectangular Prism. — This includes
three forms, viz., orthopinacoids 100 Miller; ooPco N'aTi-
mann (a); the dinopinacoids 010 Miller, ( ooPoo ) Naumann
(6); and the basal pinacoids 001 MiMer, OP Naumann (c).

100. Bight Prism on Oblique Rhombic Base. — ^This prism
consists of the positive orthodome 1 ool MUchdly 101 Miller ,

Poo Naumann (v) ; the negative orthodome loo 1 Mitclielly

101 Miller, -Poo Naumann; and the clinopinacoid ooloo
Mitchell, 010 Miller, ( ooPoo ) Naumann,

A series of derived pyramids may be obtained from this
prism also by multiplyingthe principal axis, when the

symbols will become 1 com, 1 com, ooloo .

101. Pseudoprisms. — It is evident that if the four planes

of the positive hemipyramid hM, hM, hkl, hkl, are present in
any crystal to the exclusion of the negative hemipyramid, or
vice versa, the resulting figure will have all the appearance
of, and, in fact, will be a rhombic prism. This will be still
more striking if the ends happen to be closed by pinacoids.
To distingui^ such forms from the true prisms it will be
Well to name them as I have done.

. Whatever the appearance of the combination, the symbols
will, of course, be those belonging to the respective hemi-
pyramids.

102. Hemihedral Forms. — ^These may, of course, be pro-
duced by the development of contiguous faces in pairs in any

of those "forms" which have four planes, i,e,, hM, hM, lloo ,
Iwoo , mloo , ool 1, or oolm. They may very well be indicated
by prefixing the sign e to the symbol of the form in question,
<>r ii^ the pie^iuiev constantly adopted by ITaumann^ thus y.

96 UINEBALOGT.

It shoold, however, be noted that the sign ahM and SkU have
been specially applied to those pairs of faces in the hemi-
pyramids hkl and hkl, where h has the same sign, whether
positive or negative. Thus in fig. 366 irhil will indicate the
pair of planes ee, and ahkl vill indicate i i. Bhombio
sphenoids may result from a combination of the planes hkl,
/iM'with the planes h^l, hkl; or of the remaining four planes
of the oblique octahedron.

In fig. 365 the crystal is projected in a plane parallel to
the principal, .but not parallel either to the orthodiagonal or
clinodiagonal axes. In the Jbllowing figures the plane of
projection is parallel to the principal and clinodiagonal, and
normal to the orthodiagonal.

Fig. 3GG. Fig. 367.

103. Sphere of Prpjection, — To draw a map of the sphere
of projection for this system on the projection last described
take 6 as a centre, fig. 367, and draw a circle of any con-
venient radius with fia as a radius.

Let aa' be a diameter, preferably horizontal Then make
ac = as many degrees as a + /3 (Art. 92). Then aa' = poles of
theorthopinacoidslco m , 1k> oo; 6is the pole of the clinopina-
coid odIoo ; and c that of the basal pinacoid oa ool. Bisect ae
in V, and draw vbv. Then vi> are the poles of the positive
orthodomes 1 col, 1 ccl. Bisect a'c in «', draw v'bv; w' are
the poles of the negative orthodomes. The poles of the
clinodomcs will fall on he and he'; those of the positive

OBLIQUE COUBmATIOKS,

97

' hemipTTamid 111 on frc, St>of the negatiTsbemipyrainidlll
oa bo , bv'.

In fig. 368 is givenacomplete crystal ofhnnute or clioadro-
dibe, the poles m the planes of which are marked oa fig, 369.

Fig. 370. Pig' 3?1- F'g. 372.

104. Combinations. — A series of combined forms in the
oblique system is given in figs. 370 to4I9, which the student
will do well to study. Figs. 370 to 389 represent crystals
where a-t-/3 is less than 90°; in the following figures, 390
to 419, the angle a + /3 is usually more than 90°. The letter-
ing adopted for all the figures is as follows: —
For the plane loe m a for i enl

lool hortf
mil u>

msEnucoT,

Fig. 376. Kg. 37T. Fig. 373.

Fig. 332. Fig. 3S3. Ifig. S

OBllijnE CDJ!I1INATT0^'S, 00

Bg. 385. rig. 38C Fig. 387.

Hg. 388. Fig. 3.

Kg. 301. Kg. 393. Fig. a

■E1» 3M. Kg. 395. Bg. 3

%. 398.

Fi^. 405.

OfitlQUS coUfimAtioy^

CHAPTER XIV.

FORM (Conimttcd)— THE ANORTHIC SYSTEM,

106. Axes. — ^This eystem is so called (a and opOoa), on
account of the extremely irregular character of the crystals
belonging to it. Other names are dovhly-obliqtie, triclino-
hedriCf anorthot^e, one and one membered, tetartorhomlnc,
tetartopriamatic, etc. There are three axes which are of
various lengths, and inclined to each other at various angles.
Either of them may be taken for the principal, when the
longer of the remaining axes may be called the maero"
diagonalf the shorter the hrachydiagonaL When the axes
are nearly at right angles the forms may superficially re-
semble those of the rhombic system, when two only are
nearly at right angl^ they will resemble those of the oblique
system.

106. Elements. — ^The variable conditions in this system
are evidently five, viz., the lengths of two axes as compared
with the third and the angles between the various axes.
These elements may be determined by spherical trigono-
metry, when the poles of any five planes lying in not less
than three zones are known, but the most convenient poles
are the following, viz., l.oooo, ooloo, oo ool, 1 ool, ooll.
Thus, in axinite the normals to the angles formed by planes
to which these poles respectively belong are : —

00 col loo 00=56'' 55'

00001 loo 00=97* 46'
ooool ooll =44** 43'
ooool 00 loo =89'' 55'
loDoo 00 loo =77" 30'.

107. Doubly Oblique Pyramids. — Much ingenuity has
been expended in describing these, but they rarely if ever
occur in nature, and it is better to regard them as combina-

THE AHOBTHIC SITSTEH. 103

(ions of several distinct forms, each consisting of a pidr of
aunilor pUaes oppositely situated as regards the centre of the
cr^taL

Thus the doubly ob-
lique octahedron, fig.
420, is a solid bounded
by four pairs of equal
and aimilflp Bcalene tri-
angles. These octa-
hedrons are rqjarded
as combinations of the
four forma composed of
the planes e, e', e, „e "■"■ *""

(with their respective opposite planes). These forms taken
separately are called tet^in-pyramids.

The general symbol of the -whole octahedron may be hM,
that of Kaumann is P. The symbols of the various separate

111 HI
ill ni
111 111
111 ill

lit and MUUr. JUanam

111

iP

Of course, octahedrons of several distinct kinds may be
derived from these by lengthening or shortening either
one or two of the parameters, as ^ready described under
the oblique system; but as there are very few minerals
crystallizmg in tids system — less than a dozen whosa
forma have been numerically determined— ^ we need not
devote any spacs to them
herp.

108. Doubly Oblique
Ftisms. — These also i
best studied as combination's
of open forms. Fig. 4'21
represents the doubly ob-
lique prism of 3nd order
with its axes, where the ■

plane a is one plane of the form Ico co (or the hrac/ty

101 uiNEkALOfir.

pinacoid), b of the form ooloo (or the maeropinacoid), e of
tlie form oo osl, or the basal pinacoid. The eymbols are as
follows 1 —

Brochj^inocoid, laott) MilcheS, IM MiBer, tuVo) Ndumann.
Maeropinacoid, eoluo MiicRell, OIH MiUer, oopooffaamann.
BwudpinBcaid, a aii Mitc/xll, Wl Miller, OF Sfamiuum.

Derived oblique prisms are of nian^ kindB, indeed any
tbree pairs of planes whose poles do not all lie in the same
zone circle may produce such a prism.

109. Donbly Oblique Sphenoids. — These are produced by
the development of one-half the planes of the doubly oblique
octahedron alternately, i.e., they are combinations of two
forma instead of four. They rarely occur in nature, and
there would be little advantage in devoting fspam to their
study here.

Fig. 422. Fig. 423. Fig. 424.

110. Sphere of Projection.— This is drawn in varions
podtionH, Bficording to the peculiar character of the ctystals
to be illustrated. In general the figures of this system are
best projected on a plane, perpendicular to the axis of the
Kme Ico 00 , Iso 1, by lines parallel to that axis. Kg. i22 is
the sphere of projection of anorthite drawn in this manner.
The poles of the zone just referred to fall then on the circle,
■while that of the plane aoo 1 is seen near the centre at c.

Figs. 423 and 424 are crystals of amrthUe, whose poles are
indicated by the dots in ^. 422. Figs. 123 to 430 are all

AtroBTaic ooubilfATioKe 105

^wn dn th« same pngecti<m. In figs. 431 to 433 a difiereat
projection ia chosen, in order to ahov numerotia small planes
whidi would not otJierwiue be vety well seen.

106 ttlN£kALOQir.

^ In all the £gares the vaxioos symbols are indicated by the
Same letters^ viz.: —

loo 00

=

a

12oo

r:

r

loOQO

^

a

13«>

=

z

QoloO

^^

h

1300

—

z

odIoo

^^

6

13oo

—

2'

QOQOI

=

c

1300

z^

«/

111

=

e

131

zz,

•

1

ill

=1

t

2aol

—

X

111

=

c'

2oo3

=

9

ill

zz

«/

ooll

■

zz

d

lloo

^

m

21oo

zz

h

iioo

r:

m

2100

—

h

lloo

=

m'

od21

= .

n

lloo

ziz

m,

oo21

:zz

n

lool

=

y

221

=

u

Tool

—

it

241

n

V

121

:^

8

>301

7^

w

J*

CHA.PTER XV.

FOBM iConUmedi-^THE HKXAOONAL SYSTEM.

HI. AxeSy etc — ^This system is so called because of the
numerous hexagonal prisms which occur in it. It is also
called rbowhohedral becayse of its numerous rhombohedron^,
and rrumotrimetricdl and three amd one aadal from the- pro-
perties of its axis. There are four axes, three of which lie
in one plane, are inclined to each other 60^, and are of equal
length, while the fourth is at right angles to them, passes,
through their intersections, and is of variable length. The
three equal axes are called lateral, the fourth axis prmcijxd.*

112. An^lar Element. — ^The angle made by the principal
axis with the myrmah to the planes of the chief pyramid
occurring in any particular substance crystallising in this
system is' called the am/gvlar element of that substance, as
described in Art. 56. It is the only variable element in the
system, and fix)m it the typical forms and the lengths of the
axes or peramein^ may be derived. Th6 angular eteMelit
differs widely in different minerals, from 27° 20' in tourmor
line to 81° 20' bxparisite.

113. HolohedrfJ Fonns — Pyramids.— These are of three
orders as foUows : —

* Professor Miller refers the forma of the " rhombohedral ** system
to three axes which coincide with the normals to the planes of the
principal rhombohedrons. These three axes will be, of course, of
eciuallenffth, and equally inclined to each other, but their inclina-
tion will differ in each particular substance, and will depend upon
its angular element. This system is more consistent with those
already described for the other systems, and is decidedly better for
calculation. But the system of four axes is believed to give in its
f onnulsB a clearer view of the relations of the yarious forms to eaijfh
other; besides which the principal axis is of great natural import-
ance, as it is the optic axis of ali the transparent substances crystal-
lising in the systojus.

108 HIKERAIOor.

1. Double aix-fiiced pTmmid of Ist order. This forni is
bounded hy twelve equal is(»celes triangles; each, plane cuts
two of the lateral axes at equal distances from the centre,
and the principal axia at its extremity. The symbol there-
fone is 111. Pig. 434 ahowB the situatioa of the axes in a
crystal where the principal axis is much longer than the
laterals, fig. 440 where it is very little longer. The symbols
of this form will be 111 Mitckdl, F Navmann. Brooke
and Miller regard this pyramid as a combination of the two
distinct rhomboids which will be described hereafter as its
hemihedral forms. The situation of the axes, as viewed &om
above, is seen in fig. 435.

2. Double six-faced pyramid of 2nd order. This also is
bounded by twelve equal isosceles triangles^ it only differs
from that just described in the position of the lateral axes;
fig, 436 shows the sitaation of the axes in the pyramid of
second order, the symbols of which are 121 Jlitchell, 521
Miller, F2 Jfavmaim. Each plane cuts the principal axis
and one lateral axis at normal distances from the centre, and
two other lateral axes (prolonged) at twice the normal dis-
tance, as shown at oo. A double six-faced pyramid thinf
order will be described later as a hemihedral furm,

Fig. 434. Fig. 436. Fig. 437.

114. Derived Pyramid*. — From each of the orders of

TBK EEZAOOtTAL STSTEH. 109

pyramids just described a series of p;Taini(la raay be derived
"bj multiplying the principal axis by any number greater or
lesB than unity. For derived pyramids of the 1st order the
general symbols will be lln» Mitchell, Tm ffaumann; for
those of the second order I2m Mitchell, mB2 Nauvtawi,
hM Miller.

116. Prisms. — Eacb order of pyramids has its correspond-
ing hexagonal prism whicb results 'when the principal axis
is multiplied by infinity. Figs. 43S and 436 serve to show
the dtuation of the lateral axes in the two orders of hex*
agonal prisms. A third order of hexagonal prisms Till be
described hereafter as a hemihedral form.

Tlie symbols for those of the 1st order are lloo Mitchell,
ojP Nawmann, 211 MiUer; for the 2nd order I2aa Mitcheli,
0C.P2 Namnann, Oil MUler. These prisma are really open
or incomplete forms, they may be regarded as combinations
of the planes just described with the basal pinacoids a> a>I
MitcheU, OP Ifaumann, 111 Miller,

116. Diliezagonal FytamidB. — These are bounded by
twenty-four equal scaime triangles, as shown ,
in fig. 437, but they are not known to occur
as complete forms in nature, the symbols are
1 mn Mitchell, mPn I^aumann. The situation
of the lateral axes is shown in fig, 438; when
m = 2 it might be mistaken for a combina-
tion of the pyramids of Ist and 2nd order. ^ 43S.

117. Dihexagonal FrlBm. — This is an open form, having
the same relation to the dihexagonal pyramid as the hexa-
gonal prisms have to tlie double six-faced pyramids. The
symbote are Inoo Mitchell, coPn JVoumann. The dtuation
of the lateral axes may be seen in fig. 438.

118. Sphere of Prtgeotion.— With C as centre, and any
convenient radius, draw the circle M|, Gj, ete., fig. 439.
Starting from Mj, mark off Mj, etc., equd to the radina.
Join Mj, M^; M^, M^; Mg, M^; then the lines so produced
will represent the lateral axes of the crystal, and the point
C the pole of the plane on col, ie., the north pole of the
E^ihere of projection, while M^, Mj, etc., will be the poles <^
the planes 121 situated on the equator; bisect each of the

110 UIKBIIALOGT.

kroa M„ M^, etc, in 0„ Oj, etc., ihea tlia points Q will be
the poles of the planes 1 loo ; those of Iml will lie between
m and G- on the equator, the
actual position depending upon
the value of m. The poles of
the pyramidH Hot will lie on
the Imes O, e, etc., those of the
pyraniida 1 2m on the lines M,,
c, eto., those of the dihezagonal
pyramids Imn within the spaces
M, Q, e, the positions varying
with the angnlar element of
the crystal and the valae of m
orm.
119. Eemihedral Fonos. —
lig. 439. These are of two kinds, those

with parallel and those with inclined faces. The parallel-
faced forma are the rhoinbohedrons, derived from the double
tdx-f(u»d pyramida of let and 2iid orders; the double six-
faced pyramid of 3rd order; the hexagonal scalenohedron
derived from the dihext^nal pyramid ; and the hext^jontd
priam of 3rd order derived from the dihexagonal prism.

The hemihedral forma with inclined faces are the double
three-faced pyramid, derived from the double six-faced pyra-
mids of 1st and 2nd orders; the double six-faced trapezohe-
dron from the dihexagonal pyramid; and the triangular
prism from the hexagonal prisms of lat and 2nd order.

130. Rhomhohedrous. — ^These are hemibedral forms of the
double six-faced pyramids, and they occur in series corre-
sponding with the different pyramids. For each pyran i 1
'there are two rhombohedroos, distinguished as positive anj
negative. Thus, iigs. 441 and 442 represent tl)e rhombo-
hedrons derived from the pyramid 111, fig. 440. The
'positive, fig. 441, corresponding with the shaded planes in
tig. 440, the negative with the unshaded planes. The
rhombohedrons are bounded by six equal rhombic planes,
having twelve equal edges. If we place one so that the two
ithree-faced solid angles which are formed by the union of equal
singles of the rhombic faces are upright, its principal axis
'will then be vertical oa it joins these angles. In the rhombo-

TOE HEXAOOSAL lYaTEM. Ill

bedron derived from the fyramid of 1st order the latere
rxes will then join Uie central points of tboBe edges which
»je not polar, i.e., which do not form part of the 4£re&-&«ed
solid angles just mentioned. The symbols are ± [2!] Mitchell;
±?or±R Ifaumann. Miller's symbol for the positive
rhoinbohedron is 100; for the negative rhombohedron 122.

Similar rhombohedrons may be similarly derived from all
the other double six-faced pyramids, i.e., by developing the
planes alternately. Their symbols vill be those cf the
respective pyramids modified as above.

Fig. 440. Fig. 441. Fig. 442.

131. flcalenohedrojis.— These are derived from the dihex-
agODal pyramids by developing alternate pairs of faces, the
upper pairs also alternating with the lower ones. Like the
rhombohedrons they may be either positive or negative.
Figs. 443 and 444 show the positive and negative scaleuo.
hedrons derived from the dihexagonal pyramid, fig. 437.

The lateral edges of the scalenohedrona correspond with
the edges of certain rhombohedrons which may be inscribed
within them, as In figs. 445 and 446. The symbols are
derived from those of tiie dihexagonal pyramid in the usual
manner. It is evident that the principal axis of the scaleno-
bedron must have a certain ratio to that of the inscribed
rhombohedron; this ratio is often simple, *.&, it may be 2,
3, 4, eta, times as loi^ This being ^e case its general
symbol is sometimes written 3R, 3R, 4R, eta Miller's
symbol for the acolenohedroDS is wUikl.}

132. Double Six-faced Pyramias of Srd Order.— If the
alternate upper planes of the dihexagonal pyramid are pro-
duced to meet the corresponding lower planes and the other
planes are suppressed, the resulting form will differ only in
the position of its lateral axes from those of the 1st and 2nd

112 HnrXBAUMT.

ordera; hj mokiiig the priiu^ial axis equal oo a hezagonal
prism of 3rd order raaalts. From these Srd order pjrramida
rhomboliedzonB and donble ljiree4^ced pyramids may be pra-
duoed by deTeloping alternate planes only, but these will be
tetartohedral forms.

Fig. 446. Fig. 446.

123. The Double Siz-Faeed Trapezohedron is produced
by developing alternate upper planes of the dibexagonal
pyramid and oppoiUe alternate lower planes. Ihe resulting
figure ^ a double six-faced trapezobedron. By developing
one-half of these planes alt^Tiately we obtain a double three-
faced trapezohedron, which ia also a tetartohedral form.

From the double six-faced pyramids of Ist, 2nd, and 3rd
orders, double three-faced pyramids may be obtained by
developing alternate upper planes and their oorresponding
Inwwr plitnes. In the case of the 1st and 2nd ordera of

HEXAGONAL COMBINATIONS.

113

pyramids they will be hemUiedral in that of the 3rd order
they inll be teUxrtohedral forms.

124. Three-faced Prisms. — ^From the hexagonal prisms
of all three orders triangular piisms may be producMsd by
developing alternate planes. Those so produced from prisms
of 1st and 2nd order will be hemihedral, those from the 3rd
order are tetartohedral forms.

125. Combinations. — ^In the following figures 457 to 475
the lettering indicates planes having symbols as below: —

c

—

00 col

M

=:

128

6

s;

IIOD

B

=

+ [^]

B

=

-

rill"]

L 2 J

z

~

+

Mm

L S J

z

z^

-[?]

d

^:z

11771

e

—

12m

f

2=

lf7iao

9

=

Imn

126. Prisms and Pyramids.— Kg. 447 is the pyramid
and prism lll + lloo; fig. 448 the same with the addition
of 00 ool; fig. 449 is the pyramid 111 with the prism i2oo;
fig. 450 two pyramids of 1st order 11m (dandd); one pyra-
mid of 2nd order {e); the prism of 1st order lloo (G); prism
of 2nd order 12ao (M), and the basal plane oo ool (c); ^g. 451
shows a pyramid of 1st order 11m (d); prism of 1st order
11(X)(G); of 2nd order 12oo (M); the dihexagonal piism
Imn (y% and the basal plane oooo 1 (c).

127. Prisms and Bhombohedrons.— Fig. 452 is a com-
bination of the positive rhombohedron fi^] with the hexagonal
prism 12qo ; fig. 453 is the same with the chief axis incr^used,
and rather differently placed; fig. 454 is the prism lloo with
the rhombohedron [^^j; fig. 455 is the prism 12oo with the

same rhombohedron; fig. 456 the same with the addition of the
rhombohedron [^]; fig. 457 is the rhombohedron pi^] with
the rhombohedron [*|"] ; fig. 458 the rhombohedrons [*^] and

128. Shombohedrons and Scalenohedrons.— Fig. 459 is

the prism lloo, the prism 12oo, the rhombohedron pp],

another rhombohedron [*~], and the scalenohedron Imn;

fig. 460 is a rhombohedron [^], w ith the scalenohedron \mn*

13—1 H

Tig. 447. Fig. 448. Kg. 449.

Fig. 452. Kg. 453. Fig. 454.

Kg. 466. Kg. 467, I

SeXAaONAL C01IDINATI0S8. 1 1 5

Tig, 461 ia a rbomboliedron and sc&Ienoliedron; fig, 463
ascalenohedFon'andprisin; fig, 463 a BcalenohedrooEuid prism
of different order.

Fig. 463. I^ 464. Fig. 46S.

Fig. 464 is a very complex ciystal of calcite, in which the
foUowing planes appear: —

B, the riiombohedrou f^] = ? It. Aaumann

J, the BCBlenohedniii

t^]

: 4B

0, thepritm 11°?

116 HIKBItAlOaT.

Fig. 405 ia a complex cryBtal of quartz, lowing the
following planes —

d, d", (T, <r, Four pyramidB of lit order,
«, A three-faced pyntmid. •

w, V, tf, X, Four double three-faced trspezohedrom.
M, Planes of the prism 12i» .

The following series of figores 466 to 497 is projected on
a plane perpendicular to the principal axis hj lines parallel
to that axis, and at right angles to the plane of projection,
according to the plan adopted b; Messrs Brooke and Miller.

Fi^. 472,

fiSXAGOkAt (MltBlDATIONS.

lllHE&A.1.00r.

^^3.

&EXAGOKAL COMBINATIONS. 119

In the foregoing description of the hexagonal system, we
have but rarely given the symbols adopted by Professor
Miller, because there is seldom anything like a parallelism
between them and the symbols used by Mitchell or Naumann,
owing to the totally different axes employed in the two cases.
But we may here note the symbols of the planes indicated
below, which will serve as keys to the interpretation of the
forms most likely to be met with, viz. : —

MUchell

Naumann

MUler

Form 111

=

P

= 100 + 122

„ 11m

—

mP

- Ikk

±m

=

±Ror ±|-

= 100

„ 12«

:::

ooPj

:= Oil

„ II* '

—

ooP

= 2if

» »»!

=

OP

^ 111

121

=

PjOrRoo,

= .521

12m

=

wiP2 or niRo© '

= JiH

±P?]

=

^ormR

= hkk

Incfo,

=

ooPn

= hki

Imn

zz

niPn

= likl

±r-v]

=

±[T]

a tKH

CHAPTER XVI.
OF MACLES A3KT) THE IBBEOULABITIES OF CRYSTALS.

> 129. Hacles, Twin-crystals^ or Hemitropes, are groups

of two or more crystals, which appear as if mutually inter-
secting each other, or sometimes as if a single crystal had
been cut in two in a certain direction, one part turned round
a certain number of degrees, and then re-united. The axis
around which the portions move, or may be supposed to
move, is called the ttvinrcixis, and the plane of movement the
tunnrpla/ne. Thus, if the octahedron, fig. 498, be cut in. two,
in the direction of the dotted line or twin-plane b b, one-half
rotated on the axis c c through 90% and the two again united,
a macle like ^g. 499 will result, a form which is frequently
met with in spinel, alum, and other minerals. Of course,
no such division and re-union has really taken place ; the
whole crystal having taken that form from its first origin.

Little is known of the crystallising forces, and almost
nothing of that branch which leads to the formation of twin-
crystals, but the results of this action are very common,
and it is found that the twin-axes of macles are always
inclined to each other, and to the principal axes of the
different parts, in certain definite directions for each mineral
specie^, the crystals of which affect the macled form.

130. Cubical Macles. — Figs. 498 to 505 are macles occur-
ring in the cubical system. Figs. 498 and 499 have already
been referred to. In fig. 500 the twin-planes are parallel to
one of the faces loo oo ; this form occurs in fluor occasion-
ally; it shows that it is not necessary that the members of
a twin system should be exactly composed of hcUves of the
forms fiom which they are derived. In fig. 501 the twin-
plane is 111, the macle shows faces of both cube and octa-
hedron, and occurs in cuprite. Fig. 502 is a common macle
in pyrites,

Macled crystals may generally be recognised by their re-

UACLES 6E twin CftTSTALd. 1^1

Entering anglea, but occasionally, as in fig. 603, ttiere are no
rfr«ntermg angles. This is a nutclo of ihJe rhombic dodeca-
itedron; tiie twin-plane, as before, is parallel to one of the
planes 111, and the angle of rerolution is 90°. Here, too,
ec is the twin-axis, and b 6 the twin-plane. . ~ '

FigB. 604, 505, represent interpenetrating tetrahedrons of
fahUrz, the twin-plane being 111.

181. Tetragonu Hacles. — ^Examples are given in figs. 506
to 610 which occur in casiiteriie and rviUe. The last figure
muob lesemblea an hexagonal combination.

123

HlHBIUlOaT.

ISS. Bbonbio Mifllea are given in figs. 611 to 521. A
made of cAa£»ciis is given infig. 511; ftavroUie ia Bg/L 613,
513; hmtmonito in fig. 514j cenuaiU and Araganita in figi.
515, 516, 517j marcagUe in fig. 518; wolfram in fig. 619;
chryigier>/t in fig. 520; iMrmoiome in fij^ 521.

1UCLE8 OS XVIN CSTSXAI&

F!g. S19. Fig. fi2Q;

138. Oblique Maolea are g^ven in figa. S23 to 525, all of
which occur in orthoclage. ^g. 525 ia the same aa fig. 524,
seen from ahore.

1S4. Anorthio Hacles occur freqaeutly in oBUe, oligoclaaef
and anorthite. A macle of albite is given in fig. 526.

Hf, HexagOBal Mules. — These are very common, espect<
ally in quartz and caldte^ Figs. 627, 528, are met with in

iU liiHEEAtoSt.

tiie former; fig. 629 is a very frequent made in tihe latfer.
Many most beautiful hexagonal macleB occur in snow crystab,
eight of these fotma axe giTeu in £g. £30.

Fig. 524. Fig. 525. Fig. 526.

In macles composed of two members whose crystallograpLic
' axes are continuous with each other, so that the phmes of one '
are continued without interruption into the other, we cannot
always determine with certainty whether Buch combinations
should be regarded as macles or not Thua,infig. 631, we may
either treat the whole crystal as a combination of the prism
and complete rhombohedron, or, viewing it aa a twin, with a
twin-plane b b, we may regard tbe upper planes as belonging'
to the poaitive, and the lower to the negative rhombohedrcin.
•. la this case it is impossible to determine with certainty; but'

IBItEGDLA.BniEB OF CSTffTALS.

Rp. 533,

126 MINERALOGY.

there are sometimes in such cases irregularities or partial
modifications which enable us to determine the question
with absolute certainty, such as tiie pknes m in fig. 532,
'' which is a made o{ pyrargyriie figured by Dana.

1S6« Twin-planes. — ^In the cubical system the twin-plane
is usually parallel to the plane 111, sometimes to loo 1.

In the pyramidal system the chief twin-planes are parallel
to the faces loo oo , lloo , loo 1, loo 3, 111, 113.

In the rhombic ^system the principal twin-planes are
parallel to the planes lloo , odIoo , loo qo , Iqo 1, loo #, loo 2,

loof, ODll,llJ,lft.

In the oblique system the chief twin-planes are l«3oo
oo ool, 31oo , loo 1, loo 2, coll, Qol2.

In the anorthic system the twin-planes are ooloo and
00 odI. There are also twin-planes perpendicular to a plane

passing through the poles of the zone lloo, ooloo, lloo, to
those of the zone oo ool, loo 1, loo 2; and of the zone loo oo ,

lloo, lloo.

In the hexagonal system the chief twin-planes are parallel
to ooool, lloo, 121, +Bf +iR, -JB, -211.

Usually a movement through 90^ would bring one member
of a twin system into a position corresponding with that of
the other, but in some instances a movement of 180^ would
be necessary.

187. Irregularities of Crystals.— These are very frequent,
especially in the case of large crystala We can oidy describe
a few in this chapter. They may arise from the imperfect
development of certain planes, the curvature of ^< planes/'
striations, roughnesses, druses, or interruptions; they are due
probably to a want of room to crystallise, or a too free or too
scanty supply of material, the aggregation of small crystals,
etc. Certain combinations also give rise to deceptive forms
which are often very difficult to detect.

138. Imperfect Development — Examples are given in
figs. 533 to 536. Figs. 533, 534, represent common forms
in alum; fig. 535 is a crystal of spinel, described by the
Oomte de Boumon; fig. 536 is a crystal of garnet figured
by Dana. Many other examples might be given. In all
such instances of imperfect development, f.6., of a greater

IBRCflPtABITIEB Or 0RT8TAU.

Fig, S42.

128 MIKBRALOUT.

development of cdmilar planes pn some sides of the centre
than on others^ the angles made by the different planes (or
their normals) with each other are unchanged. Thus, in
iigs. 533 and 534 the angles included between adjacent faces
will be accurately those of a perfect octahedron, 70° 32' be-
tween normals, or 109° 28' between adjacent faces.

139. Curvature. — Examples are common in the diamond,
dolomite, cJudyhite, and many other minerals. Figs. 537 to
539 have been observed in the first; figs. 540, 541, 542, in
the second; fig. 543 in cinnabar '^ fig. 544 in qua/rtz.

140. Striations, etc. — ^Frequently certain planes of crystals
are seen to be striated in certain directions, as, for instance,
the quartz crystals last figured. These striations may really
be looked upon as a series of minute modifications or alter-
nations of planes, as in the crystal of heryl from the United
States, fig. 545. Fig. 544 would appear to owe its curvature
to a similar series of alternations on a much smaller scale.
Mjany crystals are rough on certain planes, and sometimes
this roughness takes ^e form of a series of minute planes
belonging to the same, or to a related crystal form. Thus,
many octahedrons di fiuor have their planes roughened with
minute triangular or square planes/corresponding to the
faces 111 and loo go , such crystals have been called complex,
compound, or polysynthetic. Another kind of druse is when
a crystal is sprinkled oyer on certain planes with minute
separate crystals of the same or another mineral. This is
really a coating deposited after the supporting crystal was
fully formed, and i^e mineral is said to be invested. We
shaU again refer to these druses in the chapter on pseudo-
morphs.

We may here refer to the peculiar results of such alter-
nations of form as are illustrated in figs. 546, 547. The
first is a skeleton cube of halite or roch-scdt^ found sometimes
in nature, it also occurs in Jluor. The somewhat similar
octahedron of goM, fig. 548, is also remarkable for the peculiar
stalactitic formation of its lower portion.

141. Deceptive Forms. — ^Many of these have been already
referred to and illustrated. Thus in the cubical system the
tetrahedron and octahedron so closely resemble the pyramid
\\\ aQ4 the sphenoid ^^ of chalcopy4te^ belonging to tb^

SECEPTITE FOKUS.

129

pyramidal syatem, that they can only b« distinguished by

careful meaaurement. The irregularly developed octahedron,
fig. 535, closely resembles an hexagonal form, 'while the rhom-
bic dodecahedron and deltohedron, fig. 536, might easily be
mistaken for a pyramidal combination, and the imperfectly
developed crystal of alum, fig. 533, for a rhombic crystal.
An irregularly developed rhombic dodecahedron, like fig. 548,
is undistinguishable from an hexagonal prism tritb trihedral
summits. Again, many combinations in the pyramidal
system closely resemble others belonging to the rhombic
system when the ortbo- and brachy-diagonals happen to be
nearly equal. The same may be said of anorthic forms, one
of whose lateral axes happens to be nearly at right angles
to another, and we have seen that the macle of rutUe, fig,
510, exactly resembles an hexagonal combination.

Rhombic macles are often scarcely distinguishable from
hexagonal prisms and pyramids, as in the cases of Aragonite,
eerttadle, nitrt, etc., tig, 517. The macle of harmolome, fig,
521, exactly resembles a pyramidal prism. In all such cases,
as we have already said in referring to the difficulty of

130 HINEBALOQT.

determining whether some macles of ccdcite are macles or not,
search must be made for roughnesses, striations, variations of
cleavage, slightly developed modifications, and the like, when a
clue will generally be found leading to the true determinations.
142. Homology of diflferent Systems. — As the position of
any plane is accurately known when its intersections with
three imaginary lines, called axes, all of which do not lie in
one plane, are known, it would not be difficult to apply a
system of three equal axes crossing each other at right angles
to all crystal forms. Thus, supposing the respective lengths
of the axes of the form 111 in the pyramidal system to be
as 1 : 1 : 2, and those of a form 111 in the rhombic system
to be as 1 : 2 : 3, then, still referring all planes to three axes,
as in the cubical system, the symbols of the planes will be
112 and 123 respectively. The planes of the cube, tetragonal
prism of second order, and of the prism on rectangular base
in the rhombic system will be :

Cube, loOOO, OoloO, loOOO, OOIOO, OOQol, ooool

Square prism, loooo, oolx, loo go, ooloo, oooo2, oooo2

Bectangular prism, 2oo oo , ooloo , 2x oo , ooloo , oo oc3, oo qo3.

Similiar modifications might be arranged on this principle
for all possible forms; but, of course, if the lengths of the
axes did not happen to be in such simple raiios (and it is
very seldom that the ratios are so simple), the symbols would
be greatly encumbered by fractions. It will be observed
that the parallelism of the symbols for the cube, with those
for the rectangular prism (rhombic system), is less than with
*those for the square prism (tetragonal system). In the case
of oblique, anorthic, and hexagonal crystals the parallelism
of symbols would be still less, and there would be more
difficulty in determining them, but it would evidently be
quite possible to use such a universal system of axes.

We may here, however, call attention to the similarity
which has been shown to exist, by Professor Dana, between
certain cubical and oblique forms. Figs. 648, 549,. will
serve to illustrate his remarks. Pig. 548 is a rhombic dode-
cahedron, placed so that one of the trihedral angles is nearly
at the summit or apex; and fig. 549 is a crystal of orthoclase.
The planes of the rhombic dodecahedron are in each case

HOHOLOOT OF DIFFEBEITr STSTEHS. ISl

marked d, but, in fig. 549, there are in addition three planes
marked a, which correspond to the faces of the cube ; three
corresponding to the deltohedron 122, which truncate the
edges of the rhombic dodecahedron, and finally, one of the
planes of the octahedron appears in the figure marked o.

If a dodecahedron be so placed that an octahedral axis,
i.6., the line between the apices of two of the trihedral solid
angles is vertical, it is then a six-sided prism with trihedral
summits. If now this axis be inclined 8° 6' (as in fig. 548),
in one of the diametral planes of the six-sided prism, it will
have the inclination of the axis of orthoclase (as in fig. 549),
and this 8^ 6' is the greatest amount of divergence from the
dodecahedral angles that occurs in the species. The planes
dd are inclined to each other at angles near 120^, and as
there are twelve in the crystal, they may be taken as their
representatives although somewhat distorted.

The planes «, twelve in number, also have angles with each
other near 150^, and they correspond with those of the
deltohedron.

The planes a make angles with the planes d which are
near 135^, the angle of the true cubical combination, and as
they are six in number they may obviously be compared
with the cubical fiaises.

Finally, the plane marked o is inclined very nearly 125** 16'
and 144** 44' respectively to the cubic and dodecahedric
faces, these being the correct angles for the true cubical com-
binations. These planes, therefore, may obviously be compared
with the octahedral faces, but as they are only two in number,
it is evident that six are suppressed.

The two cleavages in orthoclase are parallel to dodeca-
hedric faces, and the twin-planes are either dodecahedric or
cubic. Dana observes : " These relations hold true also for
the triclinic felspars, the only peculiarity in which is that
the principal section has slight lateral obliquity, so that the
two (dodecahedric) cleavage planes incline to one another
93^ 15' instead of 90°"

143. Dimorphism. — Some mineral substances, such as
carbonate of lime and sulphide of iron crystallise in two
distinct forms, having different axes. Thus calcite and
AragonUe are dimorphous forms of carbonate of lime, the first

132 SHNERALOGY.

crystallising in the hexagonal, the second in the rhombic
system, "hi like manner sulphide of iron crystallises in the
rhombic system in Trnvrcasite, and in the cubical system in
pyrites, Blende (cubical), and w'urtzite (rhombic); senar-
montite (cubical), and valentinite (rhombic); and barytoccUcite
(oblique), and hromlite (rhombic), are additional examples of
dimorphism. Some substances, as titanic oxide and silica,
crystallise in three distinct forms, and are said to be tri-
morphous. Sulphide of silver affords another example of
trimorphism as it crystallises in the cubical system in argen-
tite, in the rhombic system in daleminzite, and again in the
rhombic system, but with diflferent parameters in acanthite.
These diflferent forms of crystallization in the same mineral
substance are believed to indicate different conditions exist-
ing at the time of the formation of the substance — ^thus
the temperature or pressure existing at the time of crystal
lization of carbonate of lime may determine whether the
resulting mineral shall be calcite or Aragonite,

144. Isomorphism. — ^When substances of diflferent chemical
composition crystallise in similar or nearly similar forms,
they are said to be isomorphoics, thus the carbonates of lime,
iron, magnesia, and manganese are isomorphous, since they
all crystallise in the hexagonal system, and the angles of their
chief rhombohedrons do not diflfer from each other, except
by a very few degrees. Moreover, it is found that these
carbonates are rarely alone in natural mineral substances, a
portion of the one carbonate being almost always " replaced "
by one of the others. In any isomorphous group the similarity
of form is generally accompanied by a similarity of other
physical properties. In the cubical system isomorphism is, of
course, very common, although not universal. The more im-
portant isomorphous or vicarious mineral substances (capable
of replacing each other in atomic proportions without affect-
ing the resulting form), may be arranged as follows : —

I. Simple Substances —

a. Muorine and chlorine, iodine, bromine.

b. Sulphur and selenium.

c. Arsenic, antimony, tellurium, bismuth.

d. Cobalt, iron, nickeL

e. Copper, silver, mercury, gold.

t»OLTMEROUd ISOMORPHISH. 133

n.— A. Oxides— Formula, RO or R—

a. Idme, ma^esia, protoxide of iron, protoxide of man-
ganese, oxide of zmc, oxide of nickel, oxide of cobalt,
potash, soda, yttria, oxide of cadminm, oxide of cerium.

h, lime, baryta, strontia, oxide of lead.

B. Oxides — Formula, RjO or Rj—

a. Sub-oxide of copper, suD-oxide of lead.

C. Oxides— Formula, RjOg or R^ —

a. Alumina, peroxide of iron, peroxide of manganese,

oxide of chromium, oxide of bismuth.
h. Oxide of antimony, arsenious acid.

• •

D. Oxides — Formula, ROa=R —

a. Oxide of tin, oxide of titanium.

E. Oxides— Formula, R„05=Rj —

a. Phosphoric acia, arsemc acid.

F. Oxides— Formula, R03=R—

a. Sulphuric acid, selenic acid, chromic acid, manganic
acid.

b, Tungstic acid, molybdic acid.

III.— A. Sulphides— Formula, RS2=R"—

^ a. Sulphide of iron, sulphide of zinc.

B. Sulphides— Formula, RS=R' —

€L Sulphide of copper, sulphide of silver.

0. Sulphides— Formula, R3Sa=R^" —

a. Sulphide of antimony, sulphide of arsenic.

145. Polymerons Isomorphism. — Scheerer states that in
compounds containing magnesia, protoxide of iron, and the
other oxides mentioned (II. A a) above, part of the base may
be replaced by water, in the proportion of three equivalents of
water for each equivalent of base replaced. Thus, 3MgO, SiOg,
2MgO, SiOg + SHgO, and MgO, SiOg + BHgO are isomorphous
compounds, the first being chrysolite, the last serpentine. This
theory has been adversely criticised by Haidinger, Naumann,
and Bammelsberg, and, on the whole, seems still to need con-
firmation from facts.

146. Ag^egates. — Crystals and crystalline grains of the
same or difierent minerals are often intermixed regularly or
irregularly together in great quantities to form rock-masses.
These are called mineral aggregates. The most important
are the granular or granitic^ porphyritic, oolitic, saccharoid,
and /oZta^ec^ aggregates. The study of these belongs to
Petrology.

CHAPTER XVIL
OF MMORPfflSM, PSEUDOMORPHISM, and PETRIFACTION.

147, Pseudomorphism. — In the last chapter we have
described certain "deceptive forms," which, while apparently
belonging to one system of crystallization, really belong to
another. We have now to describe certain bodies, called
Pseudomorphs, the results of processes of change which are
constantly going on in nature, and which occur in forms
different from those properly belonging to the substances
in question.

148. Hypostatic* Pseudomorphs.— These are formed by
the deposition of mineral matter upon the surface of pre-exist-
ing minerals. When the new matter is deposited only on the
exterior, as in the case of the " druses " already refeired to,
the term exogenef is used; when upon the interior of a
hollow mineral the term esogensX is applied; and if in both
the term amphigene,% Exogene pseudomorphs often retain
the original mineral within them, partly or completely filling
up the interior; but sometimes they are mere hollow shells,
empty, or filled with water, or with mineral solutions. Some-
times these hollow shells have been subsequently filled with
new mineral substance, and still later the shell itself has been
removed, when the final result is a new body having pre-
cisely the form of the original. All these different stages
have been observed, for example, in pseudomorphs of qtmrtz,
aiterjluory in the Gwennap Miaes; chalybite, after gypsum,
at Virtuous Lady Mina

* 0)r0$r«r0$ (hypostaios), to be sustained.

t tl {ex\ without ; and ymfiat (ginomai), I am born.

:|: If (es), within; and ytMfuu.

§ ttfipi {amphiit both; and ytftfuu.

METASOMATIC PSEUDOMORPHS. 135

149. Metasomatic Pseudomorphs.* — In these, which are
the most common, as well as the most important, pseudo-
morphs, some only of the elements present have been usually
changed by removal or substitution. The original crystal
appears to have been surrounded, by causes which we need
not now study, by media, such as air, water, hydrofluoric
acid, etc., capable of afiecting its decomposition, slowly or
rapidly as the case may be. This medium has removed
some of the ingredients or components, and has sometimes
given up some of its own at the same time, which remain
behind to form part of the new substance. If these changes
are slow they may not affect the original form of the sub-
stance acted on. This kind of pseudomorphous action has
often taken place on a very large scale; thus there is good
reason to believe that over large tracts of country the fel-
spar, forming a constituent part of masses of granitic rocks,
has been completely kaolinised by hydrofluoric acid acting
from below, and large veins of carbonate of iron have been
converted into limonite or hematite by the action of the air
or of surface waters.

When the result has been the formation of a more highly
oxidised or electro-negative substance, as in the case of chaly-
bite or iron pyrites converted into hematite, the new bodies
are called anogenef pseudomorphs; when the change is in
the opposite direction, as of felspar into kaolin, or rock-salt
into gypsum, they are called katogenel pseudomorphs.

150. Petrifactions. — These also are processes of pseudo-
morphism of several kinds. The most general is that in which
a thin layer of mineral matter is deposited upon an organic
substance so as to preserve its external form, as in the cases
of the so-called petrifying springs of Matlock and elsewhere.

If now the organic substence forming the interior of such
a petrifaction should be removed by solution, or should shrink
and fall to powder from decay, and the cavity be filled up
anew with mineral matter, and finally the original coating
be removed, a cast having the form of the original substance
would be left. Of this nature are the sandstone tree-stems

* fitra (meta), together with (used sometimes in the sense of
transposition); and o'v/ia (soma), a body or substance.

t ttf» (ana), upwards. t Kotret (toa), downwards.

136

UlKEftALOOr.

which occur so abundantly in the coal measures, and the
pyritous casts of ammonites found in the gault.

The above are analagous to the hypostatic pseudomorphs
already described; but there is a more perfect kind of petri-
faction analagous to the metasomatic pseudomorphs. This
results from the infiltration of mineral matter, usually
carbonate of lime or silica, into and between the cells of
organic substances before decay has set in. In such cases
the minutest details of structure are sometimes preserved,
and the character of a fossil wood may be readily determined
after it is completely silicified. Most fossils have been petrified
by one or other of the methods above described.

The following list of pseudomorphs, which, however, is far
from complete, will be useful for reference : —

Htpostatic Pseudomorphs.

Graphite in

the form

of pyrites.
Aiagnesite.

Salt

tt

Anhydrite

9»

Salt.

Gypsum
Fofyhalite

tf

Salt, Ceruasite.

9*

Salt.

Quartz

l>

Fluor, Gypsum, Calcite, Baiyto-
calcite, Magnesite, Scheeute,

Galena, Cerussite, Hematite,

Pyrites, Chalybite, Felspar, Copper.

Prase

)f

Calcite.

Eisenkiesel

99

Calcite.

Chalcedony

>>

Barytes, Fluor, Calcite, Magne-
site, Pyromorphite.

Camelian

)>

Calcite.

Homstone

>»

Muor, Calcite, Mica, Chalybite.

Semiopal

f*

Calcite.

Lithomarge

>>

Fluor.

Pyrites

>>

Quartz, Stephanite, Pyrargynte.

Marcasite

>»

Pyrargynte.

Chalybite

}>

Barytes, Calcite, Magnesite, Selenite,
Fluor.

Malachite

»y

Calcite, Cerussite.

Chrysocolla

»>

Cerussite.

Felspar

»)

Calcite.

Meerschaum

99

Calcite.

^rolusite
Hausmannite

>>

Calcite, Magnesite.

f )

Calcite.

Manganite

»>

Calcite.

Ffidlomelane

$9

Barytes, Muor, Pharmacoeiderite.

HYPOSTATIC PSEUDOMORPHS.

137

Cassiterite

CeruBsite

Stilpnosiderite

Hematite

Limonite

SmitHsonite in the form of Flaor,Calcite,Magnesite, Galena,

Pyromorplute.
Fyromorphite, Felspar, Bismuthinite.
Barytes, JFluor.
Magnesite, Calamine.
Fluor, Galcite, Chalybite, Cinnabar.
Barytes, Fluor, Calcite,Magnesite,

Quartz, Comptonite, Blende,

Galena, F^morphite, Cerus-

site. Cuprite.
Barytes, Calcite, Clialcocite.
Fluor, Calcite. •

Limonite.
Chalybite.
Blende.
Galena.

Fyrites,

Marcasite

Calcite

Barytes

Celestite

Fluor

Opal

Talo

Chalcop^te.
Erubescite.

l^SEUDOMOEPHS AFTER ORGANIC FORMS.

{Petrifactions,)

Pyrites in the form of Ammonites, Shells, Wood, etc.

Croal ,, Wood.

Cnalcedony „ Animal forms (Beekites).

Barytes ,, Animal forms.

Flint ,, Sponges, Shells, etc.

Metasomatio Pseudomorfhs.

a. By Loss of Components.

Calcite in the form of Gaylussite.

Quartz „ Heulaudite, Stilbite.

Kyanite „ Andalusite.

Hornblende.

Cuprite.

Pyrargyrite.

Steatite

Copper

Argentite

ft
t*
ft
tf

b. By Addition of Components,

Gypsum m tTie form of Anhydrite.

Mica

Valentinite

Anglesite

Hematite

Limonite

Malachite

Erubescite

Chalcopyrite

9t
Jt
ft
ft
f »
ft

Finite.

Antimonite.

Galena.

Magnetite.

Hematite.

Cuprite.

Chalcocite.

Chalcocite.

138

IflNEBALOGt.

e. By Exchange of Components
Barytes in the form of Witherite and Barytocalcite.

Fluor

Caldte.

Gypsum
Calcite

Calcite.
Gypsnm.

Magnesite
Chalcedony

Calcite.

DathoUte.

Jasper
Opd

Hornblende.
Angite.

Cimolite

Angite.

lithomarge

Topaz, Felspar, Nepbeline.

Kaolin

Felspar, Porzellanspath, Leacite.

Mica

Andalnsite, Felspar, Scapolite,
Tourmaline, Coraierite.

HardFablnnite,,

Cordierite.

Airoasiolite
Fanlnnite

»

Cordierite.

ff

Cordierite.

Esmarkite

)>

Cordierite.

Bonsdorffite

tf

Cordierite.

Chlorophyllite

'.»

Cordierite.

Weissite

If

Cordierite.

Praseolite

ft

Cordierite.

Pyrargillite

ft

Cordierite^

Gigantolite

}»

Cordierite.

Finite

y>

Cordierite.

Prehnite

It

Analdme, Mesoty{>e, Leonhardite.

Talc

t*

Chiastolite, Kyanite, Couzeranite, Fel-
spar (?) Pyrope.

Steatite

99

Magnesite, Spinel, Quartz, Andalnsite,
Chiastolite, Topaz, Felspar, Mica,
Scapolite, Tourmaline, Staurolite,

' Garnet, Idocrase, Augite.

Serpentine

}»

Spinel, Mica, Garnet, Augite, Chon-
drodite. Hornblende, Olivine.

Hornblende

tt

Augite.

CUorite

tf

Febpar, Gramet, Hornblende.

Ppolnsite
Mansmannite

if

Manganite.

tt

Manganite.

Valentinite

tt

Antimonite.

Stibiconite

tt

Antimonite.

Kennes

tt

Antimonite.

Bismnthochre

tt

Aikinite.

Minium

tf

Galena, Cemssite.

Galena

tt

Pyromoiphite.
Galena, Cemssite.

Fyromorpliitc

^ M

Cemssite

91

Galena, Anglesite, Leadhillite.

Wnlfenite

tt

Galena.

Magnetite

>»

Chalybite.

Hematite

91

Gdtmte, Pyrites, Pharmaoosiderite.

UETASO\tATtO fSEtfDOKOtlPfid.

13d

Limonite

StilpnoBiderite

Pyrites

Melanterite

Green Earth

Pseudotriplite

Wolfram

Erythrite

Melaoonite

Pitchy Copper Ore

Coveflite

Malachite

Chessylite

in the form of

Chalybite.

Marcasite, Scorodite.

Vivianite.

MispickeL

Pyrites.

Augite.

Triphylline.

Scheeute.

Smaltite.

Chalcocite.

Chalcopyrite, Fahlerz.

Ghalcopyrite.

Chalcopyrite, Fahlerz.

CHAPTER XVin.
ON MEASURING CRYSTALS.

161. Constancy of Angles. — Generally, whatever the
apparent irregularity of single crystals or combinations of
forms, the angles made with each other by similar planes are
constant within very narrow limits. It is only by measur-
ing these angles that numerical values can be assigned as
the indices of the different planes, and sometimes the syat&m
of crystallization can only be determined by such measure-
ments. To measure these angles goniometers are used, which
are of two different kinds, the one measuring the angle
directly by contact, the other indirectly by reflexion.

152. Carangeot's Goniometer. — ^This is a contact gonio-
meter ; it consists of a small semicircle divided into degrees,
and a pair of movable arms of brass jointed at their inter-
section. In using this instrument the movable arms are
applied to the crystal, as shown in ^g, 650, until the two
arms rest accurately upon the planes in a direction at right
angles to the included edge. The screw at the intersection
is then tightened, and the arms are applied to the brass
semicircle, as shown in flg. 551, when the number of degrees
of inclination may be at once read off.

Fig. 550. Fig. 551.

This mode of measurement is sufficient for the beginner,
but it is difficult to get results within a degree or so, and it

UEASTTBINO 0BT8TALB. Ill

is not applicable io very small crystalB, nor to the r»«iiteTiiig
angles of macles. *

1S3. Wollaston's Ganiometei. — In this iaBtrument the
crystal is attached to a graduated circle which is made to
revolve bo that the image of a window bar, or other object
seen by reflexion from one of its surfaces, is brought to coin-
cide with the image of a second signal seen directly in the next
face. The following description of the principle of the in-
strument, and of the mode of using it is, with the accompany-
ing figures, taken from Mr, Brooke's description in the
Encycloposdia Metropolila/na:—'

" This purpose ia effected by causing an object, as the line
at m (fig. 652), to be reflected successively from the two
planes, a and b, at the same angle. It is well known that
the images of objects are reflected from bright planes at the
same angle as that at which their rays fall on Uiose planes ;
and that when the image of any object reflected from a
horizontal plane ia observed, it appears so much below the
reflecting surface aa the object itself is above.

Fig, 552.

" K, therefore, the planes a and 6 (fig. 552) are successively

brought into such positions as will canse the reflexion of the

line m from each plane to appear to coincide with another

line ab n," the crystal must have been revolred through as

■e-eDtering angles is to take a

142 HINEBALOOT,

many degrees as the angle included by the planes ah, '^ To
bring the planes of any crystal successively into these rela-
tive positions the following directions will be found useful : —

" The instrument, as shown in the sketch (fig. 553), should
be first placed on a pyramidal stand, and the stand on a
small steady table about 6 to 10 or 12 feet from a fiat win-
dow. The graduated circular plate should stand perpendi-
cularly from the window, the pin GH being horizontal, not
in the direction of the axis, as is usually figured, but with
the slit end nearest the eye.

" Place the crystal which is to be measured on the table,
resting on one of the two planes whose inclination is required,
and with the edge at which those planes meet nearest and
'^T^ -^^ ^ parallel to the window. Attach

3

^^ * \ a portion of wax, about the size

> ^ of d, to one side of a small brass

Fig. 654. plate, e (fig. 554); lay the plate

on the table with the edge, /, parallel to the window,
the side to which the wa^ is attached being uppermost,
and press the end of the wax against the crystal till it
adheres; then lift the plate with its attached crystal and
place it in the slit of the pin, GH, with that side uppermost
which rested on the table. Bring the eye now so near the
crystal as, without perceiving the crystal itself, to permit the
images of objects reflected from its planes to be distinctly
observed, and raise or lower that end of the pin, GH, which
has the small circular plate on it, until one of the horizontal
upper bars of the window is seen reflected from the upper
or first plane of the crystal, corresponding with the plane a,
and until the image of the bar appears to touch some line
below the window, as the edge of the skirting-board where
it joins the floor.

"Turn the pin, GH, also on its own axis, if necessary,
until the reflected image of the bar of the window coincides
accurately with the observed line below the window. Turn
now the small circular handle, S, on its axis, until the same
bar of the window appears reflected from the second plane of
the crystal, until it appears to touch the line below; and
having, in adjusting the Jirst plane, turned the pin, GH, on
its aacis, to bring the reflected image of the bar of the window

MEASURING CRYSTALS. 143

to coincide accurately with the line below, now move the lower
end of the pin laterally, either towards or from the instru-
ment, in order to make the image of the same bar, reflected
from the second plane, coincide with the same line below.
Having ascertained, by repeatedly looking at and adjusting
both planes, that the image of the horizontal bar, reflected suc-
cessively from each plane, coincides with the observed lower
line, the crystal may be considered ready for measurement.

"The accuracy of the measurements taken with this instru-
ment will depend upon the precision with which the image
of the bar, reflected successively from both planes, is made to
appear to coincide with the same line below; and also upon
the or 180° of the graduated circle, being made to stand
precisely even with the lower line of the vernier, when the
first plane of the crystal is adjusted for measurement. A
wire being placed horizontally between two upper bars of
the window, and a black line of the same thickness being
drawn parallel to it below the window, will contribute to the
exactness of the measurement by being used instead of the
bar of the window and any other line.

"Persons beginning to use this instrument are recom-
mended to apply it first to the measurement of fragments at
least as large as that represented in ^g, 554, and of some
substance whose planes are bright. Crystals of carbonate
of lime will supply good fragments for this purpose, if they
are merely broken by a slight blow of a small hammer.

" For accurate measurement, however, the fragments ought
not, when the planes are bright, to exceed the size of that
shown in fig. 653, and they ought to be so placed on the
instrument, that a line passing through its axis should pass
also through the centre of the small minute fragment which
is to be measured. This position on the instrument ought
also to be attended to when the fragments of crystals are
large. In which case the common edge of the two planes,
whose inclination is required, should be brought very nearly
to coincide with the axis of the goniometer; and it is fre-
quently useful to blacken the whole of the planes to be
measured, except a narrow stripe on each, close to the edge
over which the measurement is to be taken."

Prof. Naumann has invented a modification of that part

144 UINERALOGT.

of tbe instrument used for adjusting the crystal to be
measured^ which is shown in fig. 555. He also adds a small

mirror on the stand below the crystal
with its face parallel to the axis aa,
and inclined 45® to the window,
when the lower signal can be dis-
pensed with.

The student will often find it
Fig. 655. sufficient to attach the crystal by

a piece of wax to the axis a directly, and give it the
further adjustment by the hand. The only use of the
parts C to H is to enable the observer to place the crystal
accurately, i.e., with the intersection of the planes to be
measured parallel to, and as nearly as possible coinciding
with, the centre of the axis. This is efiected when the re-
flexion of the horizontal signal in both faces appears to be
parallel to the included edge.*

154. O'Reilly's Goniometer.— The goniometer just de-
scribed is extremely accurate, in good hands giving results
whose errors are less than the variations of the crystals them-
selves. It is not however sufficiently portable for field use.
Prof. O'Reilly has recently invented a reflecting goniometer
which is little larger than a carpenter's pencil, and which
gives exceedingly good results. To economise space the
graduation is made to wind in a spiral around a thin cylinder,
and the crystal is attached by wax directly to the principal
axis of the instrument.!

155. Reading Crystals. — The student should at first
practice on models belonging to the cubical system, com-
mencing with simple holohedral forms, then proceeding to
hemihedral forms and combinations. He should then com-
pare the simple forms of the other systems with those of the
cubical system, and gradually pass on to forms of greater
complexity. He should also accustom himself to observe
and sketch small natural crystals.

* An easily constructed form of reflecting goniometer, devised by
Mr. J. B. Hannay of Glasgow, is described and illustrated in the
Mineralogical Magadne for April 1877.

+ The instrument is fully described and illustrated in the Pro^
ceedings of the Royal Irish Academy, Vol. I., Sec. xi., No. 6.

UEASURIITQ CRYSTALS. 146

In order to read forms -witli advantage, he should endea-
vour to place the crystals or modele on any convenient stand,
EO that one axis, tie principal if there ia one, is vertical,
and another facing him directly right and left By looking
^own from above on a crystal ao placed, he will have it
placed as in Miller's figures belonging to the tetragonal,
rhombic, and hexagonal systems. When there is a distinct
cleavage he -will, if the Bpeciee ie known, get a good indica-
tion of the planes, as the cleavages are always parallel to
certain planes.

156. Useful Bules. — The following simple rules will be
useful to the young student in making out crystal forms.

Two pairs of planes, forming angles of 90° with each other,
may occur in all the aystems except the anorthic; three pairs
forming acch angles with each other are only likely to occur
in the cubical, pyramidal, and rhomhic systems.

Angles of 60" and 120° occur more often in the cwfttco? and
hexoffonal systems than in any of the others.

Angles of 109° 28', 70° 32', and 135° are almost oharao-
teristic of the cubical system.

Zones should be recognised as soon as possible, as they
will greatly assist the determinations of the less charaotetistic
plan^ Any one plane may, of course, be
common to two or more zones.

For any plane d of a zone ada, fig. 656,
the sum of the angles between d and the
two adjoining planes aa equals 180° + the
inclination of a upon a. In the case re-
presented in the figure the angles are —
a\d = 136'
d A o = 135^ Fig. 658.

Bnm = 270°=180°+90*, whichUttdrwthe
iuclinittion ota \a.

The angles between normals to the extreme planes of any
series, forming taot more than half a complete zone, will eqnal
the sum of the angles made by the normals to the different

CHAPTER XIX,
PHYSICAL PROPERTIES— CLEAVAGR

167. The crystalline form of such minerals as occur in dis-
tinct crystals is a character of much importance, but perfect
crystals are generally rare, and many important minerals do
not crystallise at all. The study of the other physical char-
acters of minerals becomes therefore of the highest importance
to all students of minei'alogy.

The chief physical characters of minerals, excludmg form^
which has been dealt with in great detail, and the optical
and chemical characters to be described hereafter, may be
arranged under the following heads : —

Cleavage.
Structure.
Fracture.

Frangibility (tenacity).
Hardness.

Touch.

Specific (travity.

Magnetism.

Electricity.

Cleavage. — This is the property possessed by many crys-
tallised and crystalline minerals, of splitting in certain direc-
tions more readily than in others; affording shining surfaces,
sometimes curved, but usually plane, called cleavage planes.
These cleavages are spoken of as perfect when very smooth,
less perfect or imperfect when the new surfaces are somewhat
irregular. Sometimes cleavages are spoken of as highly per-
fect, very perfect, perfect, imperfect, and very imperfect. Thus,
calcite has a highly perfect and quartz a very imperfect
cleavage. •

The cleavages are usually parallel to the faces of one of
the simpler "forms," consequently, as already mentioned,
they render great assistance to the crystallographer by giving
him certain fixed points to start from in " reading " a crystal.

The student should obtain specimens of such easily cleav-
ftble minerals as galena, fluor, blende, calcite, etc., an4

CLEAVAGE.

147

endeavour to obtain from them the different cleavage forms.
Thus, from fluor he may get the octohedron and acute
rhombohedron, from galena the perfect cube, from blende the
rhombic dodecahedron, and from calcite the rhombohedron.
By laying the mineral upon a thin cushion or leather pad,
placing the edge of a stout knife so as to coincide in direction
with ^e plane of cleavage, and striking the back of the knife
sharply with a light hammer, very good cleavage forms may
be got without injuring the surfaces already existing.

file following minerals have perfect, and, mostly, easy
cleavages, parallel to the planes indicated : —

Cubical System.

r

Alabandite.

Cobaltite.

Cnbaiie.

Oahnite.

Galena.

Gersdorffite.

Hauerite.

loo 00

Maffnetite.

KaLannite.

Periclase.

Salt.

Skutterudite.

Sylvine.

Xnimanite.

Ill
Diamond.
Fluor.
llco
Blende.
Hauerite.
Hattynite.

Fyramtoal Systeic.

loo GO. ooool.

Scapolite. Anatas&

loo 00 . Apophyllite.

Idocrase. Hausmannite.

loo 1. , Kagyagite.

Anatase. Somervillite.

Braunite. Torbemite.

loo 2. Autunite.
Torbemite.

Ehombio System.

ODQOI.

Anhydrite.

Barytes.

Celestite.

Cryolite.

Dyscrasite.

Eudnophite.

Fayalite.

Leadbillite.

Lommite.

Pr3mite.

Roselite.

StemberjB^te.

Thenardite.

Topaz.

Tyrolite.

odIoo.

Anhydrite.

Jamesonite.

Niobite.

Pyrolusite.

Stmvite.

Wolfram.

148

HiyERALOOT.

loooo.

Anhydrite.

Antimomte.

Aragonite.

Atacamite.

Brochantite.

Comptonite.

Diaspore.

Epistilbite.

Epsomite.

Gathite.
Haidingerite.
Harmotome.
Manganite.
Mascagnite.
Niobito.
Olivine.
Orpiment.
PhiUipsite.
lloo.

Picrosmind.

Folianite.

Pyrolusite.

Staurolite.

StUbite.

Wavellite.

Wolfram.

Wolfsbergite.

Barytes.
Loganite.
Manganite.
Mendipite.

Mesotype.
Pyrolusite.
Smithsonite.
Strontianite.

Obliqxte System.
ooool.

Orthoclase.
Glauberite.
Klinoclase.
Lepidolite.

Malachite.
Melanterite.
Mica.
Mirabilite.
loooo.
— —^

Epidote.
Hypersthene.

Idnarite.
Spodumene.
ool«.

Annabergite.
Brewsterite.
Erythrite.
Enclase.

Gypsmn.
Heulandite.
Kottigite.
Laumonite.
lloo.
^

Valentinite.

Wavellite.

Witherite,

Monazite.
Bealgar.
Bhyacolite.
Triphylite.

TincaL

Malachite.
Pharmacolite.
Symplesite.
Vivianite.

Achmite.

Amphibole.

Arfvedsonite.

Augite.

Botryogen.

Gaylussite.

Anorthic System.
ooool.

Albite.
Babingtonite.

Christianite.
Labradorite.
ool2.
Chessylite.

ooloo.
Christianite.

Lehmannite.
Scolezite.

Oligoclase.
Sassolite.

CLBATAGS.

I4d

HSZAGOKAL STSTEaC
00 eel.

Antimony.

Cronstedtite.

Arsenic.

Covellite.

Biotite.

Eudialyte.

BismutlL

Hydrargillite

Brucite.

Parisite.

(^^Hntonite.

Fyrosmalite.

Ohlorite.

Pyrrhotite.

Comndum.

Ripidolite.

Ill ^

2=^.

Ankerite.

Diallogite.

Calcite.

Dolomite.

Chabasite.

Magnefiite.

Chalybite.

Mesitite.

Corundum.

Millerite.

Spartalite.

Stilpnomelane.

Susannite.

Chalcophyllite.

Tellnric Bismuth.

Tetradymite.

"Willemite,

12oo.

Spartalite.

11«.
Cinnabar.
Tellurium.

Millerite.

Nitratite.

Pyrargyrite.

Tourmaline.

Willemite.

Xanthoconite.

Dioptase.
erite.

j->iop

168. False Cleavages. — ^These are sometimes, and more pro-
perly, called pla/nes of union. They are formed when two or
more crystals increase so as to come in contact. In such cases
there is a sort of adhesion; but the compound mass breaks
more readily between the crystals than elsewhere. As the
broken surfaces so produced are often smooth and shining, they
may be mistaken for true cleavages. They may however be
easily distinguished, since with a true cleavage other lamellae
may be readSly split off parallel to the first one produced; but
this is not so with false cleavages.

The cleavage of rocks is frequently quite a distinct pheno-
mena to that of minerals ; but sometimes it is determined
by the prevailing directions of the constituent minerala Thus
in mica schist the plates of mica have usually a prevailing
direction, parallel to which the rock splits readily. In like
manner, in many kinds of granite, the felspar crystals have a
prevailing direction^ which determines the *^ cleavage " of the

CHAPTER XX.
PHYSICAL PROPERTIES— STRUOTUEB, Em

159. Structure. — Properly speiJdng, the decmage of crys-
tals is part of their structure^ but it is more convenient to
treat the other kinds of. structure separately. The chief
varieties of structure, as distinct from cleave^, are caUed—

Ok Fibrous, — Made up . of thin, straight, or curved fibres
lying side by side. They have often a silky lustre. ScUin
9pa/r is a name given to fibrous varieties of gypaum and aror
gonite, in which this silky lustre is very strongly marked.

b. Reticulate. — ^The same as fibrous, but the fibres crossing
each other irregularly in all directions, as in the minersd
called nwwrUmn leather.

c. Stellate. — ^The fibres radiating from centres in all direc-
tions, as in atUbite and some varieties of gypsum.

d. Radiate or Divergent. — ^The fibres diverging from each
other, but not producing complete stars, as in antimanite and
pyrohmte.

e. I/omeUar. — The mineral appearing to consist of flattened
leaves or laminae, as in branzite* The laminie may be either
flat or curved.

/. FoUaceotis or Micaceous, — ^The leaves being very thin,
as in mica and selenite.

g. Oramdar. — ^Apparently made up of minute grains^ as
in chalk or kaolin.

160. Fracture. — ^Any broken surface othei* than A cleavage
pkme, or plane of union, of two or more ciystalsi

According to its general form it may be-—

a. Conchoidcd (shell-like). — Having curved markings likeJ
those seen on the inside of many bivalve shells^ as in flint
and opal.

b. Even. — ^A surface free from marked depressions or ele^
vationsy as in dudsocUe.

*"^ ^■■■■^

PHYSICAL PROPERTIES. - 151

c. UTWvm, — ^A surface having irregular depressiorts or
elevations, as in cassiterite.

According to the nature of the broken surface the fracture
may be —

d. Smooth, as in lithomarge.

e. Splintery, as in serpentine.
/. Earthy, as in kaolin.-

g. Hachly, or covered with sharp wire-like points, as in
native copper,
161. Prangibility or Tenacity, — Minerals may be —

a. Tough, or Only broken with difficulty, as liorn-
hlende.

b. Brittle. — Parts of the mineral fly off in powder on
attempting to cut or scratch it. Very easily broken with a
blow, as tourmaline (schorl).

c. Sectile, — Thin pieces may be cut off with a knife, but
the mineral falls to powder by hammering, as chalcodte.

d. Malleable. — When slices may be cut off and flattened
under the hammer, as native copper.

e. Friable or Pulverulent. — The mineral is easily crushed
between the fingers to a powder.

/. Elastic. — ^The mineral may be bent, but springs back to
its former position when the bending force is removed.
Example, mica,

g. Fleodble, the mineral may be bent, and remains so after
the bending force is removed. Example, molybdenite.

162. Touch. — A property of some importance in the dis*
crimination of minerals. Thus, some minerals feel unctuous,
like graphite and talc; others feel ha/rsh, like axitinolite;
others, again, feel meagre, like Trmgnesiie.

163. Hardness, — ^This is a character of much importance
in the discrimination of minerals. It is usually expressed
by comparison with the following " Scale of Hardness : "— *

1. Talo.

2. Gypsum (or Rock-Salt).

3. Calcite.

4. Fluor.

5. Apatite.

6. Orthoclase.

7. Quartz.

8. Topaz.

9. Corundum.

10. DiAMONP.

The hardness of a mineral may be determined in different
ways: —

/\

163 ICIKBiULOOY.

1. £7 attempting to scratch it with the minerals in the
foregoing list successively.

2. By passing a finely cut file over the specimens, with
a rather firm pressure, three or four timea

3. By attempting to scratch the specimen with a knife.
Several trials should be made to obtain certain results, and

each method should be tried if possible. Thus, suppose the
specimen is a piece of cluUcocite. No. 2 (gj^sum) fails to
scratch it, but No. 3 (ccdcite) scratches its surface readily.
Next, reversing fche method, it is found that the specimen
under trial will scratch No. 2 readily, but not No. 3. On
trying it with the file it is not rubbed away so readily as No.
2, but more readily than No. 3. It would be sufficient to
set down its hardness at 2*5.

164. Easy as this method may seem, some precautions are,
nevertheless, necessary. Thus, in a fibrous specimen, a
scratch directed across the fibres will always indicate a lower
degree of hardness than the true one, the scratch should
therefore be parallel to the fibres, or still better, on the sur-
face of a transverse fracture.

A sound, undecomposed specimen should always be selected,
since the hardness of minerals is greatly affected by decom-
position. Many minerals are softer when first obtained, than
after they have been kept some time in a dry cabinet. In
crystals, the edges and angles are often considerably harder
than the faces, and those of the primitive fbrm than of the
modifications. The portion of the specimen selected for trial
should be, as nearly as possible, of the same shape as that of
the comparative specimens.

165. Brittleness should not be mistaken for hardness.
Many minerals which are too hard to be scratched, are yet
forced away in powder before the knife to some extent.

Some minerals contain hard particles of foreign matter
imbedded in them — ^these should not be overlooked.

166. A series of substitutes has been arranged for use
when a scale of hardness is not available; i.e. —

1. May be readily impressed with the finger naiL

2. Is scarcely impressed with the nail; does not scratch
a plate of copper.

3. Scratches a piece of copper, but is also scratched by it.

r

PHTSICAL PROPERTIES. 153

4. Is not scratched by a piece of copper, but does not
scratch glass.

5. Scratches glass slightly; is easily scratched with a knife.

6. Scratches glass easily; is scratched a little with a good
knife.

7. Is not scratched with a knife, but yields to a file.

8. Cannot be filed, but scratches a rock crystal.

9. Scratches a topaz.

10. Scratches a ruby.

167. Specific Gravity. — ^This term is used to express the
weight of a substance as compared with some other substance.
It is a character of much practical importance in Mineralogy.
Water is always the standard of comparison for minerals;
thus, the specific gravity of water is said to be 1, that of
silver 10*5, the meaning being that silver is 10 J- times
heavier than an equal bulk of water.

The specimen to be examined should be free from foreign
matter and from decay, unless it is the specific gravity of
such a specimen which is actually wanted. It should also
be free from cavities; when these are suspected, the specimen
should be powdered.

168. The following methods will' sufiice for all minerals,
the first for such as are in compact masses, the second and
third for similar masses, for small fragments, or for liquids.

1*^ Method* — a. Weigh the specimen carefully in an ordi-
nary pair of scales.

h. Suspend it by a horsehair from below the scale-pan, let

it dip well under the surface of water in r

some convenient vessel, as shown in ^g, ^ ^ A.

^

557, and again weigh it. It will be
found that fewer weights will balance it
than in the first weighing.

c. Subtract the weight in h from that
in a, the difference will be the weight of
a bulk of water exactly equal to the
specimen. Fig. 657.'

d. Divide the weight a by the difference c {a- b), the
quotient will bo the specific gravity G, according to the

formula ^^ = G.

161 HINBBALOOT.

$nd Method. — Procure a small »peci/ie gravity hoUle (or a

flmall glass beaker of the form and dze of fig. 558, having a.

mui^^ma^ thin glass plate gronnd to fit its upper edge),

n&o arranged as to hold a known weight of
water — say 50 grains. Fill it with water,
insert the stopper, and wipe it dry. Now,
make a counterpoise of exactly the weight of
the filled bottle.
Fig. 558. a. Weigh off any convenient quantity of the

Bpecioien less than the capacity of the bottle, and in frag-
ments not too large to go into it.

6. Put the weighed fragments into the bottle, taking care
to lose none. Of course, as the bottle was ali'eady ^lUd
with water, some will now run out. It is also evident that
the water which runs out must be of ex-
actly the same bulk as the mineral intro-
duced. Having again inserted the stopper
(or put on the cover), and 'wiped the bottle,
it will be found that the counterpoise,
together with a smaller number of weights
than those used to balance the fragments
in a, will produce equilibrium.

e. The difference will be the weight of
the displaced water, i.e., of a bulk of water
equal to the specimen, and the same formula

^^ = Q will give the specific gravity.

3rd Method. — Specific gravities are
often determined by means of Nicholson's
areometer, a little instrument which is
made in many forms, one of the most con-
venient of which is represented in fig.
659. This is a hollow, pear-shaped body
(a), nsually of brass, having a wire stem,
which supports a little cup (6), and '
another suspended cup below (e). The
Fig. 56% whole apparatus is so arranged as just
to sink in a tall jar of water to a mark {d) placed on the
wire stem, when a given weight, called the bala/nce weight,
is placed in the cap 6. The fipecimen to be experimented

t»fiTStCAL PlU)P£Rl?l£d. 155

upon mtist not exceed this weight, which we will suppose
to be 100 grains, the quantity marked upon the body of the
instrument.

The fragment is placed in the cup bf weights are added
until the instrument sinks to the mark d on the stem. The
difference between the weight used and 100 grains, of course,
equals the weight in air (a) of the specimen.

It is now taken from the cup h and placed in the cup c,
when, as the mineral is buoyed up by the water, the instru-
ment will rise, and more weights must be added until it again
sinks to the mark d. This latter quantity is the weight
of the water displaced by the mineral (c), and once more, by

the formula — ft = ^> "w® g^t the specific gravity of the

mineral.

When the specific gravities of two substances are known,
by taking that of a mixture of the two we may find the
relative weights of each of the components. Thus, knowing
the total weight of a nugget of gold while partially enclosed
in quartz, we may determine the weight of the gold exclusive
of the qimrtz.

Let g = the weight of gold in a nugget*
„ G = its specific gravity.
„ g = the weight of quartz.
„ Q = its specific gravity.
„ n = the weight of the nugget.
„ N = its specific gravity.
Then g+q=n,

"^^ G + Q-N-

From which equations we may obtain the following —

(N-Q)G

^-"^ G-QN*

Thus if the specific gravity of a nugget whose weight is

11 J oz., be 7-43, taking the specific gravity of quartz at 262,

and that of fine gold at 19*35, we shall have from the above

formula —

„ ^ 7-43 -2-62 19-35 1070 3452-5 ^^^.^

^=^^'^^ 19-35-2-62 ^T43"= 1243039 =^^^^^'

t.e., the amoimt of fine gold in the nugget will be 8-6107 oz.*

* Galbraith and Haoghton's Mantial of Hydrostatics*

166 KIKEBALOOY.

' Wben a mineral is soluble in water it may be weighed in
oil, alcohol, or other liquid, in which it is insoluble. The
specific gravity, of this latter liquid being known, or sepa-
rately ascertained, and that of the mineral as compared with
it being determined, its specific gravity as compared with
water will be found hj simple proportion.

If a mineral be lighter than the fluid used in determining
its specific gravity a sinker of brass may be used. Let this
be weighed, and call the weight x. Then

a+x-b'

The bubbles of air which attach themselves to the rough
surfaces of minerals when suspended in water cause them to
displace rather more water than they would otherwise, con-
sequently the specific gravity is apt to be understated. To
avoid this the bubbles should be removed by a bristle, or the
water may be boiled for a minute or so, and allowed again
to cool to 60^F. before the determination is made. Or the
mineral may be dipped in strong alcohol, and afterwards
washed in distilled water after weighing in air and before
weighing in water. In this way air bubbles will be got rid
of, and the true specific gravity may be ascertained without
difficulty.

r

CHAPTER XXI.
PHYSICAL PROPEETIES-MAGNETISM, Etc.

169. Hagnetism. — ^This property is not much used in de-
termining unknown minerals; but it is of great importance
in practical mineralogy and geology, since the instruments
used in surveyinfic are often affected by magnetic substances.
The mineral S hss most magneJpowtr is that called
magnetite, or native loadstone. It sometimes occurs in large
masses, and very frequently in minute grains, disseminated
through rocks so as to render them magnetic throughout.
In Sweden and the United States a magnetic needle,
mounted so as to move in a vertical plane, and called a
*^ dipping needle," has been used in the discovery and map-
ping of masses of magnetic iron ore which are covered with
other rocks.

This is the only important or widely-distributed mineral
which will attract unmagnetised metallic iron; but many
minerals are attracted more or less by a magnet, or will
attract a magnetised needle such a^ is used for surveying in-
struments. The ores of manganese, nickel, and cobalt have
often this property in a small degree as well a« many ores
of iron. Some mineral substances which are not naturally
magnetic become so after being heated, especially the carbon-
ate of iron, which may be thus distinguished from several
minerals which it much resembles with great ease and
certainty. .

A convenient instrument for a mineralogist is a pocket
knife — one blade of which is magnetised. Such a knife may
be used in testing fine particles or powdered minerals for
magnetism.

Ordinary magnetic substances, as iron, nickel, cobalt, man-
ganese, and their ores^ are generally attracted by either pole
of a magnet; but magnetite has sometimes distinct magnetic

108 MINERALOGY.

polarity, that is, a particular point will attract one end of a
freely suspended needle, while it repds the other end; native
bismuth and some few other substances repel both ends of
such a needle. These are said to be dtamagneiic.

170. Electricity. — Many minerals become electrified and
capable of attracting light bodies after being heated or rub-
beJi. These are said to be pyro-electrio or frictio-electric.
Friction with a feather is sufficient to excite electricity in
some varieties of blende, while most tournudinea are pyro-
electrio. Some minerals, such as topaz, will retain their
electricity for hours, others lose it in a few minutes.

A very simple and delicate electroscope for testing this
property may be made from a bent glass rod, firom which a
minute fragment of gilt paper or gold leaf is suspended by a
single fibre of silk. On approaching a substance whose
electricity has been excited by any method, the suspended
fragment will move towards it.

Electricity is of two kinds, each being the opposite or
complement of the other. That excited by rubbing a glass
rod with silk is called mt/reoua or positive, while the electri-
city developed by rubbing sealing-wax or sulphur with wool
is called resinous or negative. Nitre, fluor, aragonite, apatite,
and epidote, acquire negative electricity by friction, whilst
sulphur, wolfmm, tantaJite, mispickel, and cassiterite de-
velop positive electricity. Some crystals while exposed to
an increasing temperature exhibit positive electricity at some
points of their surface and negative at other points; while
the temperature is felling these points are charged with the
opposite electriciti^ The points at which an ascending tem-
perature develops positive electricity are called ancdogotis
poles, and those which develop negative electricity under the
same circumstances an/tilogous poles.

171. Phosphorescence. — Many minerals after being
heated, exposed to Ught, rubbed, or electryied, seem to glow
or shine in a peculiar manner if taken into a dark {^ace.
This property is called phosphorescence. Thus if a piece of
fluor-spar, especially the massive variety called chhrophome,
be placed on a fire shovel and heated over the fire, or in a
glass tube and heated over a spirit lamp, it will when taken
into a dark place be seen to shine with a bright green light.

PHYSICAL PROPERTIES. 159

If an electric shock be passed through a piece of chlorophane,
a similar phosphorescence will be produced. It has long
been observed of diamonds that, if taken into a dark room
after exposure to the light of the sun, they will shine brightly.

Minerals which become phosphorescent from heat are
sometimes called pyro-phosphoric, from friction frictto-phos-
phoric, from electricity electro-phosphoric, from exposure to
the light of the sun helio-ph^sphoric. These latter are said
to be insolarised, as is the case with some varieties of calcite.

Sometimes a pyro-phosphoric substance by repeated her.t-
ing loses its property of acquiring phosphorescence. This
may be occasionally restored by passing a few electric shocks
through the substance.

Among pyro-phosphoric minerals, some, as certain varieties
of fluor and diamond, begin to shine in the dark at a tempera-
ture below that of boiling water. A great many minerals
shine at a temperature much below a red heat.

Among minerals which become phosphorescent by friction
may be mentioned the blende from Kapnik, which shines
when scraped or scratched. Two pieces of qua/rtz will shine
if rubbed together in the dark, either in air or under water,
and some varieties of dolomite and calcite^ emit light when
struck by a hammer.

In grinding siliceous minerals, so as to make thin sections
for microscopic purposes, phosphorescent light is almost
always produced.

172. Heat. — ^We have already stated that heat develops
electricity and magnetism in minerals under certain condi-
tions. M. Senarmont discovered, in 1847, that the conduc-
tion, of heat in crystals has a direct relation to their crystal-
line form, in a manner precisely in accordance with their
relations to light.*

* Comptes Bendusy 1847, p. 708.

CHAPTER XXn.
OPTICAL PROPERTIES— OOLOUB, Em

173. Optical Properties. — ^Among those properties of mine-
rals which relate to or depend upon laght, and which are recog-
nised by the eye, colour is naturally the first to be observed.

Among other optical properties we may mention streaky
Itistre, diaphaneity or trcmsparencyf chatoyancy, iridescence^
opalescence, refractive power, and polarising power.

174. Colour. — ^The colours of minerals having metallic
lustre often afford useful aids to their recognition. In mine-
rals having nonrmetoMic lustre, on the contrary, the colour
is liable to be much altered by the presence of minute pro-
portions of accidental impurities, or from other causes, so
that it is a character of little specific importance. Many
varieties of the same mineral species are, however, named
solely from their colour. Thus schorl is simply black tour-
maline^ ^"

"Werner arranged a long series of colours to which he pi-o-
posed that all minerals should be referred. Commencing by
separating metallic from nonrmetaUic colours, he classed the
former into one group, passing from pinchbeck-brown through
bronze-yellow, tin-white and steel-grey to iron-grey and
black. The non-metallic colours were first divided into white,
grey, black, blue, green, yellow, red, brovm, and these again
subdivided. The variations of tint are so great in most
species that "Werner's colours" are not much referred to now.

175. Pleochroism. — Many crystallmts minerals appear to
be of two or more distinct colours when viewed in different
directions by transmitted light. This property is called
dichroism when the different tints are two in number, tri-
chroism when there are three tints, and, generally, pleochro-
ism. Even when the different tints f^re not evident to tbQ

OPTICAL PROPERTIES. 161

unassisted eye, they may be detected by the use of the rff-
chroiscope,

176. Chatoyancy* is a property present in many minerals,
especially in Labradorite, It consists of a peculiar chango
of colour of the light reflected from the mineral, which is
observable when the substance is sli^^htly moved about, and
which is supposed to resemble what is ^ in a cat's eye.
It is due to a peculiar internal structure in the mineral.

177. Iridescence t is a brilliant play of colour observable
locally in the fissures of many minerals when cracked, or
between their cleavage planes. It appears to be due to the
same cause as " Newton's rings," and can only be explained
to students who have a knowledge of the wnduJatory theory
of light.! It may be readily produced by heating a piece of
quartz and throwing it into water, or by striking a blow
enough to crack but not to break it. It may generally be
seen in aelenUe, and is the chief cause of the beauty oi fire*
opal,

178. Opalescence is due to a peculiar subtransparent con-
dition of matter, such as is seen in many varieties of opal.
A good idea of opalescence may be got by filling a flask with
milk and water and putting a light behind it.

179. Fluorescence is a property possessed hj Jliwr and
other substances of absorbing certain rays of the solar spec-
trum, and subsequently emitting rays of different refrangi-
bility. They consequently appear of different colours when
viewed by transmitted and reflected light. The phenomenon
was first observed by Prof. Stokes in green fluor-spar, which
fluoresces with a fine indigo-blue colour.

180; Streak. — The colour of the powder of a mineral.
When the lustre is metallic the streak is dark, ofben darker
than the colour of the mineral; when non-metallic it is
usually lighter than the colour.

Hematite may be readily distinguished from Umonite which
it often resembles, by its streak being red instead of brown.
Wolfram, too, can be at once distinguished from blende by its
darker streak. This test admits of being tried in cases where
the specific gravity cannot be easily determined, as in im-

* CJiatf a cat. t Iris, a rainbow.

t See Lees' Acoustics, Light, and Heat, p. 165.
13—1 L

162 UINERALOOT.

bedded crystals. It may also be usually tried without injury
to the specimen.

The colour of the streak of a mineral is best determined
by rubbing the specimen on a slightly roughened plate of
white porcelain, when, if not too hard, some of it wiU be
rubbed off. Very often a scratch with a knife suffices, or
rubbing with a file; but the mark thus made in the specimen,
*^ the scratch," must be distinguished from the colour of the
abraided particles — the streak — since it sometimes differs
from it very markedly, as in the case of chalcopyrite, in
which the streak is nearly black, while the scratch is yellow
and shining.

181. Lustre. — Most minerals shine with a peculiar luatrey
which differs in different species, and depends chiefly upon
their " index of refraction " and structure. The chief vane-
ties of lustre are : —

a. MetaUic, as seen in pyrites and graphite,
h. Adamantine (diamond-like), as seen in the diamond and
some varieties of qvKx/rtz,

c. Resinous, as seen in some kinds of blende and cassiterite,

d. Yii/reous (glassy), as influor and calcite,

e. Pea/rly, as in pearJrspan' and stilbite. This is often seen
on the cleavage planes of minerals not otherwise pearly. It
frequently accompanies incipient decomposition, as in Mur^
chisonite,

f. Waxy, — Seen in some varieties of tak,

g. Silky, as in " satin-spar '' (both kinds), and in most
minerals having flbrous structure.

Each of the above varieties of lustre may vajy in degree;
thus we may have —

h. Splendant, as seen in specular iron and galena.

i. Brilliant, as in galena.

j. Shining, as in dolomite.

k. Glimmering, as in serpentine.

Different kinds of lustre sometimes occur on different faces
of the same crystal, not accidentally, but as distinct qualities
of the particular faces. Such differences, for example, occur
im anhydrite. A few minerals have no lustre, these are said

OPTICAL PROPERTIES. 163

to be dvM. Many varieties of minerals have a lustre not
perfectly metallic, these are said to be sub-metallic. The true
metallic lustre is only to be seen in minerals which are
almost or entirely opaque, but not in all such.

182. Diaphaneity or H^ansparency. — ^A general term ex-
pressing the degree of transparency or opacity of mineral
substances. The several degrees are : —

a. Transparefnt — Outlines of objects may be seen dis-
tinctly through thick layers.

h. Semirtransparent — Outlines visible, but indistinctly.

c. Tranalucen/t. — Light passes through, but no outline can
be seen.

d. Sub-translucent, — light is only transmitted through
thin edges or splinters.

e. Ojpaque, — No light is transmitted.

CHAPTER XXIII.

OPTICAL PROPERTIES— REFRACTION, Exa

183. Befraotion. — ^When a ray of light falls upon a trans-
parent substance, in a direction at right angles to its surface,
it passes through the substance without change of direction.
When a similar ray, however, falls obliquely upon the sur-
face, its direction is always changed in passing through.
Thus let otty bbf cc represent three rays of light passing from
the lamp h (fig. 560) on to the plate of glass ^, the ray aa,
falling upon its surface perpendicularly, will pass through
without change of direction; while the rays bb, cc, which fall
obliquely, will be bent out of their course towards the per-
pendicular at b and c while passing through the glass ; but
will pass on in a line parallel to their original direction
afterwards.

Fig. 5C0.

This bending is called refraction, and it is possessed by all
transparent bodies, though some substances bend or refract
the rays of light more than others. ^

184. Law of Refraction.-— If we describe a circle with
any convenient radius OA, ^g. 561, and draw A'F, DG per-

KEFBAOttOK. - 16S

pendicular to A£; then it is found tliat vhaieivet the mag-
nitade of the angle A'OA, the relation between A'F and DG-
is always the same for the same transparent substance. _ A'F
is the "sine of the angle of incidence," and DG the "dne of
,, 1 t - .■ 1. J A'F = n, which is the index of

the angle of refraction; and =— ^ ^ ^

re/raclion.*

Fig. 661.
185. Double Beftnction. — On looking at a bright point
through two inclined faces of a prifim, made of a ctystal
not belonging to the cubical system, two images or ^)eetra
will be observed. This property of not only refracting raya
of light falling obliquely, but of splitting each mj into two,
is possessed by all transparent crystalline substances which
do not belong to the cubical system.f In pyramidal and
hexagonal crystals, one portion d the ray called the ordinary
ray follows the law c^ refraction, but the other portion
called the extraordinary ray is refracted — sometimes more,
sometimes less, than the other, but always in accordance with
a different and very complicated law. The refraction of

* This subject ia more fully axplained in Lees' Aanutiei, Light,
and Heat, forming put of tha present Advanced Series.

t A few cubical minerals peeeewi a pecnliarl^ modified etmctnre
in relation to this law, bat it is quite of a dif^rent nature to that
whii^ a now described.

166 HINEBALOQT.

the ezteftordinary i&y is greater than that of the ordinary
ray in apophj/Uite, xnreon, nuHe, caesiterite, brueiU, gtuirli,
h^iatite, and pffrargyrite. It is lese than liat of tie ordi-
nary ray in wndjenite, idocrtue, analaee, meUite, nitraiite,
apatite, caicUe, dolomite, pyrom&rphite, biotite, nephdite, aajt-
fMre, tovrmaiiTie, and cinnabar. In rhombio, oblique, and
auorthic crystals neither ray is re&acted according to the
" law of fiines," except in particular direotions.

As already mentioned, all transparent crystals, except
those belonging to the cubical system, possess the power of
double refraction; but only a few have it so powerfully as to
cause an object seen through thin pieces to appear double.

Fig. 562. Fig. £63.

Of all substances possessing the property of doable refrac-
tion, that called " Iceland spar," or douily refroBtiag apw —
a very dear and transparent variety of calcite — shows it
beat. It is owing to this property of Iceland spar that all
objects seen through that substance appear double, except
when seen in one particular direction, which is the optic
axis, or axis of no double refractioiL in. the hexagonal and
tetrt^onal systems the optic axis is the principal axis of the
crystal. If a rhomboid of Iceland spar, fig. 662, be placed
over a dot on a sheet of paper, the dot will appear doubled,
the ray oi being split up into the two rays ta and m, and in
whatever position the rhomboid is placed, an imaginaiy line
joining the two dots will be parallel to the principal axis of
the crystal. Let now the two three-faced solid angles, which
a/reformed by the junction o/t}iTee eqiud and mmiJar anglei,

POLABIZATION. 167

be ground down so as to produce three triangular planes
perpendicular to the principal axis, as in ^g. 563, and paral-
lel to each other, and let these planes ( oo ool) be polished.
It will be found that a dot looked at through these planes
will not appear double. In every other direction but this
there will be double refraction. In rhombic, oblique, and
anorthic ciystals, there are two optic axes, and such crystals
are said to be Maadal.

186. Polarization. — A ray of light which has passed
through a doubly refracting crystal in any other direction
than its optic axis, sufiers a peculiar change called poh/riza-'
tion. Such a ray is not again divided into two portions if
made a second time to pass through a doubly refracting crystal.
Moreover, there is for every shining non-metallic substance
a particular angle, varying with the substance, at which
it is found that such a polarised ray cannot be reflected.

Light which has acquired these two properties is called
polarised light; but these peculiar changes may be impressed
upon ordinary Hght, not only by its passing through a doubly
refracting substance, but also by being simply reflected at a
particular angle from a non-metallic reflector ; or by being
refracted at a particular angle through a series of parallel
plates oi glass or other transparent substances which do not
possess the property of double refraction, as in flg. 564 cc;
or by simply passing through a NicoFs prism, fig. 565, or a
'' tourmaline plate " cut parallel to the principal axis of the
crystal. If a crystal of tourmaline be cut into thin plates
parallel to its principal or optic axis, a pencil of light pass-
ing through will be split into two rays. One of &ese will
be completely absorbed by the tourmaline if the plate be not
too thin, while the other will pass through the plate. The
reason of this is not certainly known, but it is probable
somewhat as follows: — Regarding the ray of ordinary light
as consisting of very rapid undulations of the luminiferous
ether in every possible direction, and supposing the struc-
ture of the tourmaline plate to resemble a very fine grating,
the bars of which are parallel to the optic axis, then it is
easy to see that all the vibrations of the incident ray, except
those which are vertical like the bars, will be stopped or
absorbed; but the vertical undulations will still be trans-

168 UtNERALoar.

mitted, and consequently the light will still pass through,
although it will be much fainter thaa the original ray. If
now a second plate (or indeed any number of plat«s) be
placed in a similar position to the first {a, fig. 666), the ray of
light 'will be no farther afiected, except in so far as the want
of transparency of the mibatance ia concerned; but if it be
placed di^onally as at l, the light will nearly all be stopped,
and if as at e (the supposed "grating" being at right angles)
the light will be completely stopped. ' If a plate of tourma-
line be BO arranged that it can be made to revolve through
a complete circle, it will be found that there are two posi-
tions in which polarised light, i.e., light vibrating in one
plane, does not pass, and these are opposite each other, or
180° apart.

^fe.

Fig. 664. Fig. 565.

If a ray of light, after being polarised, be made to pasa
again through a doubly refracting crystal, it becomes depolar-
ined, and again converted into orfinary light. This property
affords a ready test of double refraction in min^^ sub-
stances. If a plate with parallel surfaces be cleaved or cut
from such a substance, and placed between two plates of
tourmaline in crossed position (fig, 566, c), in which it will
be remembered they are totally opaque, the transparency ia
restored. In addition, the plate ia brilliantly coloured if of
a certain degree of thinness, varying with the substance

F0LAAIZATIO17.

169

tested* The plate of tourmaline through which the light in
passing is polarised is called the polariser, the doubly refract-
ing substance, the depola/riser, and the other plate of tourma-
line through which it is seen, the a/nalyser. A convenient
instrument for use in testing minerals for this property of
double refraction is the tourmaline pincette, shown in fig.
567, in which two plates of tourmaline are arranged so
chat either may be rotated through any required angle.

Fig. 566.

Any non-metallic reflector placed at the proper angle, a
bundle of glass plates, or the Nicol's prism, may be used in-
stead of the tourmaline, either as a polariser or analyser; and
an instrument arranged with any two of these for observing
such phenomena, is called a polariscope.

187. Nicol's Prism. — ^This is a rhomb of Iceland
spar which has been cut across obliquely, as at AB,
fig. 565, parallel to the principal axis; the two parts
are then finely polished and cemented together again.
The action of the " Nicol " upon light is as fol-
lows : — R is a ray of ordinary light which, on
entering the Nicol, is split up into the ordinary ray
O, and the extraordinary or polarised i-ay E. O,
meeting the Canada balsam at a very low angle, is
reflected, as shown, and is so got rid of; but E,
meeting it at a greater angle, passes through, and
emerges at unaltered. For experiments on
microscopic crystals, the polariser usually consists
of a NicoVs prism, or a bundle of glass plates Fig. 567.
placed beneath the stage; a plate of tourmaline held above
the eye-piece, or a second NicoFs prism placed in the body of
the microscope, just above the object-glass, serves well for an
analyser.

188. Table Polariscope.— A sheet of glass, with its under

170

lilKfittAtOGir.

Bide blackened, forms an excellent polariser either for the
microscope or for the table polariscope, fig. 668 ; where a is
the blackened mirror fixed on the board B. In the centre of
the board is an upright pillar supporting the tube cd, the
axis of which is directed towards the mirror at an angle of
3b^° (the complement of 54^**, the polarising angle for glass).

Kg. 668.

At c is a cap having a small hole in it, and at the other end
a second cap d, supporting the mirror m, which is used for
experiments upon simple polarization of light. When ex-
perimenting upon minerals, the best plan is to replace this
with a Nicol's prism, or a plate of tourmaline. The mate-
rial to be examined, which should be from |^ to J inch thick,
is fixed over the hole with a bit of wax, and viewed through
the analyser at d. If the object is a slice from a crystal in
the hexagonal or tetragonal systems cut parallel to oo ool,
say a hexagonal prism of calcite, a black cross surrounded
by a series of coloured rings, as in ^g, 569, will be seen,
and as the analyser is made to revolve the cross will change
from black to white, and the colours of the rings will change
to their complementaries, t,e., red to a green, and violet to
orange, as in fig. 570. The intervals between the rings ai*e
smaller as the thickness of the slice increases, or, the thick-
ness being the same, as the doubly refractive power increases.
189. Circular Polarization — In quartz exceptional pheno-
mena are observed, as compared with other hexagonal crystals.
With a slice cut parallel to oo ool, there are in every position
of the analyser the rings without the cross^ the centre of the

rig. 569

m

114.571

tHE i>ICtitROiSC0P£.

m

inner ling being of one colour, which passes through all the
tints of the spectrum to its complement as the analyser or
polariser is rotated In some specimens the change is from
red to violet, as the rotation is from left to right, and in
others the reverse is observable, the polarization being rightr
homded and left-handed respectively.

With a plate of any biaxial cryBtal, Le^ belonging to the
rhombic, oblique, or anorthic systems, e.^., nitre, the double
system shown in fig. 571 is observable, when the Nicols are
crossed. If the analyser be revolved the dark cross will
become white, and will break up into two arcs as the
plate of crystal is made to rotate, iJie polariser being fixed.
The points AB are the optic axes.

190. The Dichroiscope. — ^This is an instrument devised by
Haidinger for testing the pleochromatism of minerals. It is
drawn in section, nearly full size, in
fig. 572. A is a cleavage rhombo-
hedron of calcite, having two small
glass prisms CO of 18° each cemented
on to the ends by Canada balsam.
At one end is a convex lens, or com-
bination of lenses, D, of such focal Kg. 572.
length as to show distinctly an object, about 4 inch from
the end L, seen by the eye at D. At the other is a stop
having an opening L about *12 inch square.

On looking through the prisms with the eye at D, two
images of L will be seen just in contact with each other.
The light of one image is polarised in a plane through the
short diagonal of A (or parallel to the paper), while that
of the other image will be polarised on a plane at right
angles. When a pleochromatic crystal is placed before
L at the distance of distinct vision, and the prism turned
until its planes of polarization coincide with those of the
crystal, the two images of the square opening will show
the colours of the oppositely polarised pencils of which the
transmitted light is composed, and to which the pleochro-
matism is due.

CHAPTER XXIV.

CHEMICAL CHARACTEES— TASTE, ODOUR, Era

The chief of the so-called chemical characters of minerals,
or those which depend upon chemical composition, are —
taste, odour, aolvhility, fusibUUy, and volatility,

191. Taste is a character of great importance in the case
of a few minerals.

Thus eyanosUe, goalarite, mekmterite, halite or common
salt, kalinUe, nitre, nitratite, and a few other mineral sub*
stances, may be at once known by their taste, which is in
each case very characteristic.

The chief varieties of taste observed in mineral substances
are the following : —

a. Metallic — the taste of native metals.

b. Metallic astringent — the taste of the vitriols.

c. Sweetish astringent — ^the taste of alum.

d. Saline — ^the taste of common salt.

e. Alkalins — ^the taste of nitrate of soda.

f. Cooling — the taste of nitre.

g. Bitter — ^the taste of Epsom salts.
A. Sour — ^the taste of sulphuric acid.

The only minerals which have distinct taste are those which
are soluble in water.

192. Odour is occasionally of importance. Thus many
minerals containing alumina or magnesia give off a peculiar
earthy smell when breathed upon; others, which contain
sulphur or arsenic, when broken, rubbed, or heated, yield a
characteristic smell. The chief varieties of odour are the
following : —

a. Alliaceous — the odour of garlic. It is observed on
rubbiag, heating, or breaking ores containing arsenic,

h. Horse-radish odours — the odour of decaying horse-
radish. It is observable on heating or melting substances
containing selenium.

' CHEMICAL CHAKACTEBS. 173

u. SvlphureouB — ^the odour of burning sulphur^ observable
on heating, breaking, etc., many substances containing sul-
phur,

d. Fetid — ^the odour of rotten eggs. It is given off by
some varieties of quartz, barytes, and limestone when broken
or rubbed.

e, ArgiUaceoua — clayey. It is given off by seipentine,
and other substances containing magnesia.

198. Solubility. — This is determined by treating a
powdered mineral with water, acids, or alkalies. The chief
solvents used (and the order in which they are applied) are
as follows : —

a. Water.

b. Hydrochloric acid — ^Dilute at first ; stronger afterwards
if necessary.

c. Nitric acid — Dilute at first ; then strong.

d. Sulphuric add,

e. Aqua regia — A mixture of nitric and hydrochloric acid.
/, Special solvents, such as oxalic acid, ammonia, etc.
To ascertain the solubility of a mineral, a few grains of its

powder should be placed in a test-tube or watch glass, and
warmed with a few drops of the solvent. If the substance
he freely soluble, and it is only in such cases that this test is
valuable in determinative mineralogy, the powder will rapidly
disappear. Ajiy ^ervescence, peculiar odour, change of colour
or appearance, or insoluble remlue, should be carefully noted.
Thus sulphides may often be recognised by the unpleasant
odour of sulphuretted hydrogen which is given off when
they are treated with hydrochloric acid ; while all carbonates
effervesce strongly under similar treatment with warm acid
if not with cold.

a. Water, — Sulphates, such as melanterite, and cyanosite,
and generally minerals having distinct taste, are soluble in
water.

b. Hydrochloric add, — Many oxides, as limonite and
gothit^, dissolve quietly in HCl, without effervescence or
evolution of vapour ; others, as pyrolu^ite, give off chlorine,
especially when warmed with the acid; others again, as
cassiterite, are not attacked by the acid.

Some sulphides, as blende axid antimonite, give off vapours

174 HINEBAL007.

of HgS when treated with HCl, others, as p3rrites, are not
perceptibly affected. Tungstates, titanates, molybdates, and
vanadates are only partially decomposed, the first leave a
yellow powder (tungstic aoid), the others white powders
(titanic, molybdic, and vanadic acids) ; tungstic and titanic
acids are insoluble in an excess of the solvent, the others
are soluble, A few silicates are soluble completely in HCl,
others are decomposed, leaving deposits of gelatinous or
pulverulent silica; others are not aflPected by the reagent.

The following table shows the behaviour of the most
common silicates when treated with acids : —

a. Completely solMe in dilute HCL'

Allophane. Keilhauite.

CoUyrite. Yttrotantalite.

Gismondite. Zeagonite.

b. Decomposed by HCl separating gelatinous silica,

.^IdelfoTsite. Ittnerite.

Allonite. Knebelite.

Analcime. Laumonite.

Apophyllite. Lievrite.

Barsowite. Meerschaum.

Cancrinite. Meionite.

Cerite. Mesotype.

Ohabasite. Mesolite.

Chamoisite. Nepheline.

Ghondrodite. Natrolite.

Cronstedtite. Nontronite.

Batholite. Okenite.

Dioptase. Pectolite.

Eudialite. PhiUipsite.

. Gadolinite. Schrotterite.

Gehlenite. Siderochisolite.

Gmelinite. Sodalite.

Haiiyne. Spadoite.

Helvine. Stilbite.

Heulandite. Tscheffkinite.

Hisingerite. Thomsonite.

Humboldtilite. Thorite.

Hyalosiderite. WoUastonite.

c. Gelatinise in HCl (after ignition only).

Asdnite. Idocrase.

Epidote. Lepidolite.

Garnet. Prehnite.

CHEMICAL CHARACTERS. 175

d. Separate pulverulent silica,

Amphodelite. Lepidomelane (in pearly scjJes).

Anorthite. Leucite.

Antigorite. Pennine.

Baryta-harmotome. Pollux.

Chonicrite. Pyrosclerite.

ChrysocoUa. Bnyaoolite.

Epistilbite.

e. Separaie silica, gelatinous or pulverulent, in different varieties.

Anthosiderite. Porcellanite.

Brewsterite. Pyrarnllite.

Clintonite. Scapoute.

Faujasite. Tachylite.

Labradorite, Villarsite.

Margarite. Woblerite.
Palagonite.

/. Partially decomposed only.

Acmite. Glaucophane.

Batrachite. Isopyre.

Bole. Miloschin.

GhloropaL Sordawalite.

Cordierite. Stilpnomelane.

Edingtonite. Garnet

g. Decomposed by n2S04 not by HOL

Biotite. Kaolin (after ignition).

Halloysite. Pyrocblore.

Olivine. I^rrosmalite.

Tourmaline (after ignition). Schiller spar.

Bamourite. Serpentine.

Agalmalolite. Steatite.

Ohlorite. Spbene.

Onkosine. f^opbillite.
Ottrelite.

h. Scarcely, affected by HCl or H,S04.

Albite. Eyanite.

Andalusite. Gymophane.

Aueite. Emerald.

Difulage. Euclase.

Hypersthene. Fahlunite.

Beryl. Orthoclase.

Gaator. Gtedrite.

Ghloritoid. Hornblende.

Oonzeranite. . Hypochlorite*

176 BflNEBALOGT.

Jeffersonite. Spodmneii.

Korpholite. Stanrolite.

Oligoclase*. Talc*

Petelite. Topaz.

Fhenakite. Wichtysite.

Pitchstone. Wdrthite.

Muscovite. Zircon.
Saussuiite.

e. Nitric acid, — This is chiefly used in treating native
metals, and metallic oxides and sulphides. Many of the
metals, as copper\2Ji<dihis7nuthy when so treated, decompose the
acid, and give rise to red vapours ; so also do the suboxides,
as cuprite. Sulphides often afford a deposit or floating c^ke
of sulphur ; tungstates, titanates, vanadates, and molybdates
behave as with HCl. Minerals containing arsenic and anti-
mony often afford insoluble oxides of these substances, as
white powders, Cassiterite is not affected by nitric acid.

d. Sulphuric add is rarely used as a mineral solvent,
but some silicates, as kaolin, are more readily attacked by it
than by hydrochloric acid. A few minerals, as atacamite
and chiora/rgyrite, are soluble in NHj.

c Aqua regia may be used for the decomposition of
obstinate sulphates and arsenides, it will also dissolve gold
and platinum, the latter somewhat slowly.

194. Insoluble Minerals. — ^These are very numerous — the
term is generally applied to those which are insoluble in
HCl, HNO3, HgSO^ and aqua regia ; among them we may
mention dia/mond, corundum, spinel, chromite, diaspore,
rutHe, cassiterite, quartz, chlorargyrite, ha/rytes, celestite, angle-
site, xenotime, lazulite,childrenite,amblygonite, and boracite,
besides the silicates mentioned above; of these, the silicates
are soluble in HF.

196. Fusibility. — This is a character of vpry great im-
portance, and it is convenient to have a scale of reference.
The scale of fusibility most usually adopted is the follow-
ing:—

1. Antimonite.

2. Natrolite.

3. Ahnandine, a variety of garnet.

4. Actinolite.

5. Orthoclase.

6. Bronzite.

CHEMICAIi CHARACJTERS. 177

Aniimonite is so fusible that splinters may be readily
melted by being held in the flame of a candle; while bron-
zite is infusible. The others are of intermediate fusibility.
Of course a mineral is tested perse to determine its fusibility,
as many infusible minerals become fusible on adding other
substances.

196. Volatility. — ^This is tested by heating fragments of
minerals in closed or open tubes, or while resting upon char-
coal or other "supports." Some minerals are completely
driven off in vapour by such treatment, either with or
without previous fusion, while others are quite unchanged.
Further reference to the fusibility and volatility of minerals
vrill be made in the chapter on the use of the blowpipe.

18—1

CHAPTER XXV.

CHEMICAL CHABACTERS— BLOWPIPE ANALYSIS.

197. The student of Mineralogy should have a con-
siderable acquaintance with the principles of Inorganic
Chemistry before entering upon this advanced course; as,
otherwise, his progress will be slow, and, moreover, he will
have but an imperfect appreciation of the important chemical
relations of minerals. It is also desirable that he should
have sufficient knowledge of Practical Chemistry to enable
him to make at least a qiuxMtative analysis of any ordinary
mineral substance. ^

198. Elements. — ^The world and all it contains is made
up of about sixty-eight perfectly distinct substances. These
are called elements by chemists, because hitherto they have
not been able to deconvpoae them.

Of this large number of elements many are very rare;
while the most common minerals are made up of little more
than a dozen. Those which occur most frequently in mineral
substances are the gases oxygen, hydrogen, nitrogen, chlorine,
and fluorine; the non-metallic solids sulphur, carbon, silicon,
and boron; and the metals potassium, sodium, lithium, cal-
cium, magnesium, aluminium, and iron. In chemistry, the
elements are usually for brevity and greater convenience
indicated by letters or symbols, rather than by their full
names. In the following tables the symbpls and atomic
weights are placed against the names of the respective
elements to which they belong.

* Such information may he gained from the works on Inorganic and
Practical Chemistry, forming part of **ColHns* Elementary Science
Series."

ELEMENTS AND COMPOUNDS. 179

A. — Metals.

Name. Symbol.

Atomic or Unit
Weight

Alamininm Al 27*5

Barium Ba. 137*

tBismuth Bi. 210-

Cadmium Cd 112'

CflBsium Cs 133'

Calcium Ca. 40*

Cerium Ce 92'

Chromium Cr. 52*5

Cobalt Co 65-8

Copper Cu G3-5

Didymium D 96*

Erbium E 112-

Glucinum G 95

Gold Au. 197-

Gallium G.

Hydrogen* H. 1*

Indium In 7G'

Iridium Jr. 197'

Iron Fe 66'

Lanthanum La 92*

Lead Pb 207*

Lithium Li 7*

Magnesium Mg. 24*

Manganese Mn 55*

Mercury Hg. 200*

Molybdentim Mo ^d'

Nickel Ni. 59*

Niobium Nb 94*

Osmium Os 199*

Palladium Pd 106*

Platinum Pt 197*

Potassium K 39*

Bhodium Ro 104*

Rubidium Rb 85*

Ruthenium Ru 104*

Silver Ag 108*

Sodium Na 23*

Strontium Si 87*5

Tantalum Ta 182*

Thallium Tl 204*

Thorinum Th 238*

Tin Sn 118*

Titanium Ti 60-

* Hydrogen is hero placed with the metals, because in the majority
of its properties and reactions it more resembles metals than metalloids.

Atomic or Unit
Weight.

180 KINERALOGT.

Metals — Continued.

Name. Symbol.

Tungsten W 184-

Uranium U 120*

Vanadium V. 61'

Yttrium Y 62-

Zinc Zn. 65'

Zirconinm Zr 89*

B. — Semi-Metals.

Antimony Sb. 122*

Arsenic As 75*

Tellurium Te 129*

Btsmuth* Bi 210-

C. — Metalloids.

Boron B. II*

Bromine Br. 80'

Carbon C 12-

Chlorine CI 35 5

Fluorine F 19*

Iodine 1 127'

Nitrogen N. 14-

Ch^gen 16-

Phosphorus P 31-

Sulphur S 32*

Silicon Si 28-

Selenium Se 79*5

199. CompoundB. — Elements sometimes occur in a nearly
pure state, e,g.n native sulphur and native gold. More
usually, however, two or more elements are combined
together forming eompou/nds, €.g., water, tin-ore. The more
commonly occurring natural compounds are oxides, sulphides,
eMorideSy fluorides j ca/rbonates, sulphates, silicates, a/rseniates,
and phosphcUes,

200. FormulSB. — ^In most descriptions of minerals, the
chemical composition is indicated by a group of symbols
combined into what is called a formula. Thus, cerussite or
carbonate of lead has a composition indicated by the formula
PbCOg, From this formida, and by the aid of the column of
atomic or unit weights in the above table of the elements, it
is easy to calculate the percentage composition, or the propor-
tion of lead, carbon, and oxygen present in each hundred
parts, as shown in the £lem&Uary Mineralogy belonging to
the present series.

* Bismuth la often placed "frith the semi-mefals rather Xh^n witt^
the ?netftl9,

TB& BtOWFIPX. 181

parts, as shown in the Mlementary Mmeralogy belonging to

the present series.

After making an analyma of a mineral, it is often denrable
to ascertain what formula will best
agree with the percentage obtained.
The mode of doing this is to divide
each percentage by the atomic weight
of the component in question, and
then to divide each of the quotients
obtained by the lowest. The result
of this division gives the number of
atoms of each component present in
the compound. Generally, however,
with mineral substances, the percent-
ages do not exactly agree wiUi those
proper to any formula, owing to the
impurities constantly present, and
also to the isomorphism referred to
in Art. 14:4.

201. The Blowpipe is a cheap
and very convenient Instrament for

directing the flame of a lamp or ^s^

candle, and of concentrating its power
upon a mineral so as to ascertain the
effect of heat upon it. A very con- Fig. S73.

venient blowpipe is that of Dr.
Black, shown in fig. 573. In its
cheapest form it is made of japanned
tin, and may be obtained for a few
pence. For delicate work two pla-
tinum jets of different sizes should
be used. Many other kinds of blow-
pipe have been devised, some of which
give a continuous blast, and may be
worked by the hand or the foot.
These are described in special trea-
tises on the blowpipe; but the one
above described will be found quite d
Bufficient, if properly used, for all
mere determinative purposes. Fig. 671

183

UHEILALOOir.

202. The Blowpipe Lamp, fig. S74, -whichfaasaUrge^af*
■wick, will be found to be very convenient, especially if fed
with olive oil, but a thick candle is perhaps more convenient
for traTelHng. Many persons prefer to use gaa from its
greater cleanliness, but it ia not ao good for a "reducing"
flame. If the lamp or candle be used, the wick should bo
bent in the direction in which the flame is to be blown.

The lamp shown in figs. 575 to 578, is the best which is
known to the writer, lie figures are drawn half the real
size. Fig. 575 is a vertical section of the whole lamp, where A A
is the cover, EE the body of the lamp, BB the "Freiberg"
wick, C the wick-holder of tlnplate, D the wax or composi-
tion pieces of composite candle, " night lighte," or ordinary
tallow. Fig. K76 a view &om above; fig. 577 shows the mode
of folding the wick; and fig. 678 the tinplate cover which
nerves as a stand while the lamp is in use.

iLD

Pig. B75. Fig. 576. Kg. 577. Fig. 678.

In using the lamp, it is well after lighting the wick to
direct Hie flame over the grease for a little time so as to
melt it> After use, and while the grea&e is still melted, the
wick should be pulled up about ^ of an inch before the wax
solidifies, t

203. Blowpipe Flames. — The mode of using the blowpipa
and producing the "oxidising" and "reducing" flames, and
the modes of operation in testing minerals, are fully described
in the author's Elementary Mineralogy. We merely give hero
a summary which will be convenient for reference. The com-
plete blowpipe examination of a mineral consists of eight or
more distinct testa, some of which may often be omitted after

* It haa been wrongly drawn wit^ a roavd wick,
i- TMb lamp is described by Dr. C. Le Neve Foster in tiie lUntra^
logical Magtaitie, So. 1, Aug. 1876.

BLOWPIPE OPERATIONS. 183

a little experience has been acquired. By these tests, and a
few special tests indicated or suggested by the behaviour of the
substance itself, a skilful operator can discover the presence
or prove the absence of nearly every one of the elements
mentioned in Art. 198, and can even form a good approxi-
mation to the proportions present. The fragment of mineral
operated upon called the "assay," should not generally be
larger than a mustard seed, a small assay being much more
manageable than a larger piece.

204. Blowpipe Operations. — ^The usual course of operation
is — .

(1). Heating in "matrass" or "closed tube" to observe —

a. CliazigeB of Colour, as in arseniates and phosphates of copper,
chalyhite, etc. The operator should observe whether the original
colour is restored on cooling.

b. Decrepitation, which generally takes place in anhydrons minerals
having distinct cleavage, such as blende and wolfram. It appears to
be due to the presence of a little moisture, between the laminsB of
which the minersd is composed*

e. Fnslon, which may be partial, as in many minerals of the alum,
mU, and vitriol groups, which fuse at first in their water of crystalli-
zation but finally solidif^r, leaving an insoluble residue of various
colours; or complete, as in the case of sulphur, cryolite, and a few
other minerals which fuse at a low temperature.

d, MoiBtnre, which settles in drops on the side of the tube, as in
all hydrated minerals. The student should ascertain whether this
moisture is acid, neutral, or alkaline, by means of a piece of t'Cst
paper; and whether it is acid from the first, or only when the tem-
perature is pretty high. Thus in nitra^ the water will probably be
acid from the first, but in aulpTiatea it may only be acid when a high
temperature is used.

€. Sa1)llmation.--The sublimates may be—

1. White, melting to colourless drops on heating, indicating

tellurivm; to jrellow drops, indicating sulphur; or to brown
drops, indicating seleniu/m; volatilising without melting,
indicating arsenic, etc.

2. lied, yellow, or broum, usually indicating both sulphur and

arsenic.
8. Black, metallic, indicating arsenic.
4. Grey, metaUic, collecting into drops when rubbed, indicating

mercury,

/. Vapours or Odours are best distinguished by the next operation.

(2). Heating in open tube, when a/rseniates, svUphides^ telr
lurides, aelemdea, and nitratesy will give off characteristio
odours, and deposit characteristic sublimates.

I

1^4 IflNEftALOGY.

(3). Heating on charcoal, to observe —

a. Defla^atioxi, indicating nitrates,

h. Reduction to a bead of metal showing the presence of An, Ag,
Cu, Pb, Sn, Bi, Sb, etc., or several of them together, which may be
recognised by their colour, malleability, or brittleness, as well as by
their solubility and other chemical tests.

c. Fusililllty. — This should be compared with that of fragments
of a similar size from the scale of fusibility.

d. Vapours or Odoun. — Sulphureous, indicating ^7pAury alliaceous,
indicating arsenic; resembling horse-radish, indicating selenium; fetid
or resembling rotten eggs, also indicating sulphur in a sulphide, etc.

e. Incnutatloxis. —

1. White, near the assay, little or no odour, indicating antimony.

2. White, farther from the assay, garlic odours arsenic.

3. White, yellow while hot, white malleable bead of metal in this

or the fifth operation =^in.

4. The same, no malleable bead = zinc.

6.' Yellow or orange, grey malleable hesA=ilead.

6. Yellow, red, or brovm, grey brittle bead=6Mmti^7k

7. Dark red, white malleable bead=«}7i;er.

/. Complete Volatilization, as in native arsenic, sal-ammoniac,
g. Combustion, rapid as in sulphur, slow as in graphite,
h. Flame Colouration. — The extreme tip of the flame is sometimes
coloured —

1. Blue= sulphur, arsenic, antimony t ores of copper, containing CI

or Br, selenium, lead, etc.

2. Ghreen=barium, boradc add, borates, Bud ph4)sphateSf some ores

of copper, molybdenum, tellurium, etc.

3. lied=lUhia, strontia, lime, etc.

4. Violet =potash.
6. Yellow = soda.

These results are often better seen in the eighth operation —

{. Kon-volatile residue remains.— These may be tested by the fourth
and fifth operations.

(4). Treatment with cobalt solution, — This is only to be
tised in cases when the residue or coating from (3) is white
or nearly white. A drop of nitrate of colxilt is dropped upon
the residue or coating, and it is again heated. The following
are assumed on coolmg : —

a. Blue, alumina, silica.

b. Bed or flesh-colour, magnesia, tantalic acid.

c. Cfreen, zinc, tin, titanic acid, hyponiobic add, antimonic acid*

d. Brotonish-red, baryta.

e. Violet, zirconia, phosphate or arseniato of magnesia.

BLOWt'lPE OP£tlAl:iONS. 185

«

If a bright intense glow is observed on beating, airontia,
lime, magnesia, or ssinc are probably present.

(5). Treatment with carbonate of soda on charcoal. — ^This is
adopted when the residue from (3) is not white. The reducing
flame should be used, and the object is to obtain a bead of
metal. The metals discovered may be —

a. Gold, yellow and malleable.

b. Silver, white and malleable, not easily oxidisable.

c. Tin, the same, but very easily oxidisable.
(L Copper, red and malleable.

e. Lead, erey and malleable.

/. Bismuth, grey and somewhat brittle.

g. Antimony, grey and very brittle.

When two or more metals are present the results are often
intermediate. Should there be a strong effervescence while fus-
ing with the carbonate of soda, a silicate is likely to be present.

(6), Borax bead. — This should only be applied to the non-
volatile residue of (3). The presence of several metals or
oxides together may modify the trials produced, but the
following, with many others, are likely to be met with : —

a. Blue in both flames =co6aZ^.

b. Green in both flames =cAromti/?7i.

c. Blmek-green in OF, red in B.F= copper,

d. Violet or wmethystine in OF, colourless in ItF=man^a7teM.

e. Reddish yellow OF, dirty green 'RF=iron,

f. Yellow OF, fine green rl^— vanadium,

(7). Microcosmic bead. — ^The results in this operation are
much the same as in (6), but some of the reactions are a
little more easily distinguished, others somewhat less so in
the presence of other oxides, and some of the coloiirs are
different. Uranium, titanium, and tungsten, give in OF a
colourless or clear yellow bead ; in RF uraniwnh gives a fine
green, tungsten a beautiful blue, which is green while hot,
titamium a violet bead. Silica is insoluble in " micro'' and
remains visible in the bead.

(8). Heating in Pt forceps (or twisted in a coil of Pt wire), —
This must only be adopted with minerals which the former
operations have shown to contain neither easily reducible
metals, nor arsenic or sulphur. The student must observe —

a. Fa8il>llit7, as compared with the ''scale of fusibility."

b. Changes of Colour, as in Umonite, chalybite, eta

c. Flame Colouration, as in (3) L

186 IflNERALOOT.

d Uainietism (acquired) of the asfllty, as in chalyhite.

6. SweUlng tip of the assay, as in gUlbite.

/. Olowlng, without fusion, as in ealcite*

g, Venniciilatlon, as in vermkuUte.

A. Exfoliation, as in pyrophyllUe,

i. Alkalinity (acquired), as in the alkaline earths.

Besides, or instead of, the above eight ^^ operations/' there
may often be an advantage in using the "pyrologic" methods,
recommended by Major Boss in his recently published and
valuable work on Pyrohgy;* such as the use of boric and
phosphoric acid beads, of a plate of aluminium for sublima-
tions, and many others.

205. Special Tests. — Among special and very delicate
reactions for particular substances may be mentioned the
following : —

a. Blsmntli. — Small quantities of bismuth ma^r be detected by
mixing the powdered assay with iodide of potassium and sulphur,
and heating on charcoal. A bright red coating indicates bismuth.

6. Boron may be detected in sOicates or other minerals by makins
the assay into a paste with Turner's test f and a little water, and
heating with the tip of the oxidising flame. A yellowish*green tinge
indicates boron.

c. Oopper. — Moisten the powdered substance with HGl, or mix it
with a little moist chloride of silver, and heat with the tip of the
oxidising flame. A bright blue colour indicates copper.

d. Chlorine. — ^This is the converse of c. The assay is heated with
oxide of copper.

e. Manganese. — Fuse on platinum foil with carbonate of soda* A
green colour indicates manganese.

/. Merenry. — Mix with litharge or powdered charcoal in a dry
closed tube, and heat strongly. Mercury will be deposited on the
sides of the tube as a grey metallic coating if present.

g, Fhospliorio Add. — Heat strongly in a matrass with a fragment
of magnesium wire, or of sodium; when cold add one drop of water.
The presence of phosphorus is indicated by the disagreeable smell of
phosphoretted hydrogen^

h. Snlplmr. — Fuse on charcoal with carbonate of soda in BF;
when cold place the bead on a surface of polished silver {e.g,, a silver
coin). The presence of sulphur is indicated by a darkening of the
coin, and a smell of sulphuretted hydroffen^

i. Fluorine. — This may generally be detected by strongly heating
the assay in an open tube, m which is placed, at the cool end, a edip

* Pyrology or Pife Chemistry ^ by W^ A. Ross.
1 4j^ parts of bisulphate of potash, one part of powdei^d fltor spar^
mix.

The st*&c:iTROScoP£.

187

of moistened Brazil-wood paper. > With some silicates, as tourmaMnef
it is necessaiy first to mix the assay with phosphate of soda. The
presence of fluorine is indicated by the paper becoming yellow.

It will also be necessary in some cases to test minerals as
to their relative solubilities and other chemical characters,
as mentioned in Art. 193; but the minutiae of all such mani-
pulations must be studied in works specially devoted to
chemical and blowpipe analysis.

206. The Spectroscope. — For detecting certain substances
which are often present in very small quantities, as sodium,
potassium, lithium, calcium, strontium, barium, thallium,
csesium, rubidium, and indium, the spectroscope, fig. 579, or
some other form of the instrument, will be found very usefuL

^

Fig. 579.

It is merely necessary in general to make a paste of the
powdered mineral with HCl, to heat a little of this on a
loop of platinum wire in the blowpipe flame, and to examine
the flame with the spectroscope, when the characteristic
bright lines will be seen, as described in most works on
chemical analysis. Major Hoss has devised a '^spectrum
lorgnette" to be used for this purpose, which is made by
W» Browning of London*

CHAPTER XXVI.
DISTRIBUTION AND PARAGENESIS OP MINERALS.

207. Distribution. — Of tHe more common or more important
minerals described in the second volume of this work, manv
have been found in all parts of the world. Some, however,
are much less widely distributed, having occurred in a few
localities only, and there are many of the rarer minerals which
have, so far, only been found in one locality. Thus the
dia/moTidy horaac, dnnahar, and many others which might be
mentioned, are not known to have been found in the British
Islands; and many other minerals, which are even very
common in some countries, are here quite unknown as local
products. On the other hand, several minerals have been
found in these islands, and especially in Cornwall and Scot-
land, which have never yet been found elsewhere.

208. Paragenesis. — Some minerals occur chiefly or exclu-
sively in granite, others in diorites or schists, others again
in limestones, or in volcanic rocks. Moreover, certain
nunerals are commonly associated with other minerals, form-
ing natural groups, which in some cases appear to have been
formed contemporaneously. It is this latter kind of associar
tion, which is of so great assistancejto the student in enabling
him to recognise minerals at sight, much as specimens of the
same mineral from different locsdities may differ in appearance.
It is to this association also that the term paragenesis primanly
applies, but its meaning has been extended so as to include
all such associations of minerals in groups, or of minerals
which are congenial to each other, as miners say. In the
following lists a few of the better known examples of para-
genesis only are set down. We have distinguished those
minerals which have been found sometimes mdosed in the
species referred to by printing them in italics.

PARAGENESIS OF UIKERALS. 189

Quarts is associated with ortboclase, mka, tourmaUne, chlorite^
chalybite, calcite, dolomite, baryites, fluor, cassiterite, pyrites^ chalco-
pyrite, Um(mUe, hematite, gOthite, wolfram, cuprite, copper, galena,
blende, boumonite, gold, etc.

Caldte, with quartz, copper, chalcopyrite, pyrites, etc.

Apatite, with hornblende, axinite, magnetite, garnet, topaz, schorl^
cassiterite, wolfram, quartz, orthoclase.

Barytes, with galena, calcite, blende, chalcopyrite, pyrites, etc.

Argentite, with stephanite, arsenic, pyragynte, etc.

Cassiterite, with quartz, schorl, chlorite, mispickel, pyrites, blende,
wolfram, topaz, lepidolite, etc.

Chalcopyxlte, with quartz, fluor, galena, blende, chalybite, dolo-
mite, pyrites, calcite, etc.

Qalraa, with quartz, pyrites, chalcopyrite, blende, calcite, etc.

Fyrltee, with quartz, cassiterite, chlucopyrite, galena, fluor, mis-
pickel, limonite, cobaltite, smaltite, inverante, etc.

Cuprite, with quartz, copper, malachite, chessylite, fluor, etc.

Fluor, with quartz, wolfram, chlorite, orthoclase, chalybite, ccdcite,
etc.

Garnet, with magnetite, apatite, epidote, talc, mica, hornblende,
limonite, etc.

Serpentine, with steatite, diallage, asbestos, copper, chiysocolla^
calcite, chromite, and nickel ores.^

Snlphnr, with celestite.

Tellurium, with gold, bismuth.

Flatinum, with iridium, rhodium, palladium, eta

Gold, with quartz, tellurium minerals, etc.

Cinnabar, with tetrahedrite, quartz, calcite, etc.

Kagnetlte, with chlorite, garnet, hornblende, etc.

209. Succession of Minerals. — ^Von Weissenbach observed
long since the following succession of bands or layers of
minerals in the lodes of Freiberg, reckoning from the sides
towards the centre of the veins : —

1. Qnarti, containing pyrites, blende, galena, and mispickel con-
taining a little silver.

2. Diallog^te, with brown spar and rich argentiferous tetrahedrito,
as well as the metallic minerals mentioned in 1.

3. Chalybite, wfth fluor and barytes and the ores mentioned in 2.

4. Caldte, with rich silver ores. |

Similar successions of deposits have been observed in
Cornwall, Wales, and other mining districts, all tending to
show that, in a given locality, diflferent solutions have suc-
cessively occupied the fissures and deposited minerals upon
their walls. Every cabinet of minerals affords evidence of
the sftme natural

190 MINERALOGY.

210. Belative Age of Hineral Deposita.— -There is still

xnnch obscurily existing on this subject^ but the following
generalizations are pretty generally accepted : —

a. Tin deposits are generally older than the carboniferous period.
They appear mostly to have been, formed at great depths.

b. Deposits of gold, silver, lead, zinc, copper, cobalt, nickel, and
biBmnth ores, occnr of very dissimilar ages, but are generally more
recent than the tin deponts, and they have been foxm^ at moderate
d^ths.

c Iron and manganese ores have been mostly formed near the sur-
face, but they are of all ages, like the rocks in which they occur.

It is still doubtful, however, whether these facts rest upon
a real difference of age. If, for example, the tin deposits
were formed at a great depth, they could only come to light
after a long period of elevation and denudation, and simihir
deposits may even now be in process of formation at depths
of several miles.*

* There is good reason to believe that a certain amount of deposi-
tion of metallic ores is still going on in fissures and cavities of the
rocks. In the abandoned workings of the Cornish mines stalactitic
iron oxide is abundantly deposited, and metallic copper is often found
precipitated upon decaying 'wood. Galena has also been found in
crystals resting upon wood and iron, and a deer's horn, partly coated
with crystals of oxide of tin, is preserved in the Museum of the Royal
Greological Society at Penzance. Gold has also been found permeat-
ing masses of wood in the alluvial gold-fields of Victoria. In some
instances it is probable that the mineral substance is only transferred
over short distances, but in others it is probable that the mineral
solutions are still supplied through fissures from great depths. On
this subject Gustav Bischof s Phytdcal and Chemkal Geology may bo
studied with advantage.

CHAPTER XXVIL
ON AETIFIOIAL MINEEALS AND "MINERAL GROWTHS."

211. Amorphous Substances. — Large numbers of minerals
have the same composition as well-known artifioially-prepared
inorganic substances; and such substances might in one sense
be all termed artificial minerals. Thus the hydrated oxides
of iron, obtained by precipitation at difierent temperatures
from ferruginous solutions, are the analogues of naturally oc-
curring oxides, and so with many other chemical precipitates.
Even the botryoidal, mammillary, and other imitative forms
met with in nature, have their parallels in the substances
prepared by the chemist, or in those resulting from the
operations of miners and metallurgists.

212. Artificial Crystals. — ^We are in a great measure
ignorant of the manner in which most of the crystals occur-
ring in the mineral kingdom have been formed, as compara-
tively few have been reproduced by the chemist, and those
which have been formed by artificial means are often smaller
than the naturally-formed crystals. Crystals of quartz and
carbonate* of Hme, for instance, occur of immense size in
nature, but the crystals of these substances which have been
formed artificially are almost microscopic in character.

Crystals may be formed in a variety of ways, as for in-
stance —

a. Sublimation, or condensation from a state of vapour; ex. 8iUphur,

b. Solution, and subsequent evaporation, or cooling; ex. nUre,

c. Slow cooling from fusion; ex. bismuth.

d. Thermo-recmction; ex. diopside, moss-copper,

6. Action of vapours upon each otiier, or upon appropriate solids;
ex. ccutsUerite,
/. Electrolysis, or galvanic decomposition; ex. copper,
g. Contact witii decomposing organic matter; ex. pyrites,
h, "Spontaneous" change; ex. me so-called " mineral growths,^

As a rule, artificially formed crystals exhibit fewer modi-
fications than those which are formed naturally.

192 MIKERALOGT.

213. Crystals formed by Sublimation. — ^We have already
mentioned sulphur as an example of this mode of imitating
the operations of nature. There is good reason to believe
that sulphur, specular iron, and other minerals, have been so
formed in nature around many volcanic vents, and the latter
substance has been frequently observed as a furnace product
in cavities of slag from blast furnaces.

Arsenolite occurs in the flues of arsenic refineries as cubic
(octahedral) crystals at low temperatures, and as rhombic
crystals at high temperatures.

214. Crystols resulting from Solution. — ^Nature is very
easily imitated in this manner in the cases of substances
soluble in water without decomposition. Large crystals of
alum, cycmosite, and very many other salts soluble in water,
are easUy obtained. The modifications of the crystals, and
sometimes, as in the case of carbonate of lime, even the
system of crystallization depends upon the temperature of
the solutions at the time of the formation of the crystals, as
well as upon other causes. Bischof has shown that the great
majority of the minerals found in fissures and rock cavities
have been deposited from solutions. Becquerel has formed
apophyUite by the action of potash on selenite,

215. Crystals due to Fusion, etc. — ^Occurring as crystal-
lizations in or upon slags from metallurgical operations (fur-
nace products). The following have been observed : —

Angite. Melilite.

Ch^copyrite. Massicot.

Biopside. Melaconita-

Fayalite. Molybdeoite.

Galena. MispickeL

Gehlenite. Ortnodase.

Graphite. Pyromorphite.

Labradorite. Butile.

216. Thermo-reduction. — 1. By heating appropriate sub-
stances without fusion, and leaving them to cool, as when
" moss-copper " is formed on the surface of heated masses of
copper regulus. 2. By mixing their constituents, or sub-
stances containing them, and heating at high temperatures.
The following have been found by the experimenters whose
names sere attached ; —

ABTIFICIAL MINERALS. 193

Anatasa (O, Rose)^ bv fasing titanic acid with microcosmic salt in
the reducing flame, and then exposing for a short time to the ozidis*
ing flame.

Celestite (Oages)^ by fusing gypsum and chloride of sodium.

ChryBOberyl {Ehelman), by f usmg^ alumina, glucina, and boric add.
{DeviUe and Caron), by fusing glucma and fluoride of aluminium in
atomic proportions with boric acid.

Corundum {Ebdman), by heating sfcrongly a mixture of borax and
alumina. {Oaudin), by heating potash alum with charcoaL {DevilU
and Caron), by heating fluoride of aluminium and boric acid in a
charcoal crucible wi4^ the addition of a little fluoride of chromium
for the blue (sapphire); a little more chromium gives a red colour
(ruby).

Dlopeide [Berthier),

Forsterlte (Ebelman).

Frankllnlte {Daubrei) by fusing perchloride of iron, chloride ol
zinc and Ume.

Garnet {DaubreS, Studer)*

Idocrase {Studer),

Magnetite {DevUle and Caron), by fusing peroxide of iron and
boric acid.

Helaconlte {BeequerelS, by fusing lime with caustic potash.

Helanite {Klaproth), dv fusing idocrase.

Kimetlte (Lechertier), oy fusing the arseniate and chloride of lead
together.

Peridase (Ehelman), by fusing lime and borate of magnesia

Perofskite {Ebelman), by fusing lime with silicate of titanium.

Butlle {DeviUe)t by heating to redness titanic acid and peroxide of
tin, and subsequent heating with silica

Sphene (Ehelman).

Spinel {Ehelman)t by fusing a mixture of alumina and magnesia
with boric acid, adding chromic oxide for a red and peroxide of iron
for a black colour. {DeviUe and Caron), by heating the fluorides of
alumina and magnesia with boric acid.

217. By Passing Vapours over Heated Substances. —

Anatase, by passing steam over fluoride of titanium; also by passing
steam over chloride of titanium {Daubre4); also by passing gaseous
hydrochloric acid over titanic acid {DevilU),

Andalusite, by passing fluoride of silicon vapour over alumina,
also by passing fluoride of aluminium vapour over silica {DeviUe and
Caron).

^ Blende, by passing the vapour of sulphur over the heated oxide or
silicate of zinc ( Wurtz),

Brookite, by passing steam over fluoride of titanium {Davhrei);
also by passing steam over chloride of titanium {Daubrei),

Cassiterlte — 1. By passing gaseous hydrochloric acid over protoxide
of tin {Deville), 2. B^r passing steam over heated perchlonde of tin.
{Davbrei). 3. By passing stesSa over heated fluoride of tin {Datibre4)m
13—1. N

194 UINERALOOT.

Comndiim, by passing cUoride of alamininm vapour over Hme
{Daubre^.

Diopalde, by passing chloride of silicon vapour over magnesia
(Daubrei).

Qaleiia, by passing the vapour of sulphur over heated oxide of lead;
also by passing the same vapour over silicate of lead ( Wurtz).

Hauamannlte, by passing gaseous hydrochloric acid over a mixture
of B^uioxide of manganese and magnesia.

Hematite, by passing steam over heated perchloride of iron; also
by passing gaseous perchloride of iron over heated lime.

Idocrase, by passing the vapour of chloride of silicon over the
necessary bases {Daubre4).

Magnesioferrite, by passing gaseous hydrochloric acid over a
mixture of peroxide of iron and magnesia (Deville),

Magnetite, by passing gaseous hydrochloric acid over heated per-
oxide of iron (JDeville).

Ferldase, by passing gaseous hydrochloric acid over heated mag-
nesia (DevUle), or over heated lime (Daubred),

Batile, the same as brookite, both methods {Daubrei).*

Spinel, by passing chloride of aluminium vapour over heated
magnesia {Daubre€).

Wurtzlte, by subliming blende in a current of sulphurous acid«

218. Galvanic Action. — The best known examples of the
formation of new mineral substances by this agency are the
so-called metallic trees. Gold, silver, lead, copper, bismuth,
and many other metals are separated in the metallic state
from their solutions by the action of metals, such as iron or
sine, which are more electro-negative than themselves. There
is good reason to believe that many of the naturally-occurring
capillary and arborescent forms of these metals met with in
nature have been so formed, and the process is very easilj
imitated in the labomtory.

219. Contact with Decomposing Organic Matter.— There

is good reason to believe that native gold, pyrites, and other
minerals have often been separated from their solutions by
the agency of decomposing organic matter, t

* JTcttt^ettiZfe says that in passing steam over fluoride or chloride
of titanium^ the result is the formation of rutile when the temperature
employed is a red heat, btvohite if the temperature is between thoea
necessary for the volatilization of cadmium and zinc, and anaUue
when the temperature is a little below that of the volatilization of
cadmium. >

tSee note to Chap. XXVI., page 190.

ARTIFICIAL MINERALS. 195

Galena has been formed by saspending sulphate of lead in a bag
in water containing carbonic acid, and decomposing organic matter
together with carbonate of lime {e,g.<, a dead oyster in its shell) ;
crystals of galena were deposited upon the shell {Gages).

Blende, pyrites, malacMte, chalcoclte, and selenlte were formed in
the same way, using appropriate snlts (Gages),

Tallingite has been formed by the action of water upon ammo^o-
chloride of copper {Kane and Graham),

220. Spontaneous Change — "Growth" of minerals. — Many
minerals exhibit proof of gradual increase of size in the "lines
of growth " so often observable in crystals, the concentric
structure of stalactites and botryoidal masses. Another kind
of " growth " is seen in the efflorescence of sulphate of iron
upon pyrites, arseniat« of cobalt upon smaltite, etc. Attention
has recently been drawn to still another kind of mineral
" growth," by Professor Liversidge, Mr. T. A. Read win, Mr.
W. M. Hutchings, and others, in the Mineralogical Magazine
and the Chemical News, Mr. Keadwin states that he has,
in a great number of instances, observed in minerals, which
have never left his possession, the development of "growths"
of metallic gold, sUver, copper, etc., and he suggests that
mineralogists should pay particular attention to the state
of specimens in their cabinets at intervals, so as to detect
8uch changes as may be going on in the specimens from
time to time.*

* For full particulars on this interesting subject the student is
referred to the Mineralogical Magasaiie, No. 5, published by Messrs.
jSimpkin, Marshall, & Co., of London, and Messrs. Lake & Lake, of
Truro. Of course it is not intended, by using the term "growth"
in this connection, to convey the idea that there is anything analagons
to the growth of animals or plants.

EXAMINATION QUESTIONS.

{The figures in parenthesis refer to the Sections in whid^ (he Answers

may he found,)

1. Define accnrately the term mineral, and state what substances oidi-
2iarily classed as minerals are excluded hj this definition (1).

2. In what does a rock differ from a mineral? (2).

3. Mention ten of the principal roek'forming minerals (2).

4. What do you understand by the terms crystalloid and colloid f Give
exanmles (6).

5. Define the terms crystallised, crystalline; and cryptocrystalUne, as
applied to minerals (8).

6. What are the chief imitative forms of minerals P Give examples of
each (9}.

7. wnat are stalactites and stalagmites, and how are they formed? (10).

8. What do you understand by the terms edges, angles, and faees^ as
applied to crystals ? (12).

9. What are the axes of crystals ? (13).

10. What are the elements of crystals ? (14).

11. What do you understand by crystallographic notation? Give an
example showing the application of the different symbols adopted by
Hitdiell. Miller, and Kaumann (15, 16).

12. What are the normals of a crystal ? (18).

13. What do you understand by the terms zone, zone-plane, eone^cirele,
and zone-axis as applied to crystals ? (19).

14. What is a sphere of projection ? (17, 27).

15. What is a crystallographio/orm ? What are holokedral, hemihedral,
and tetartohedral forms ? (20).

16. What is a combination in crystallography ? (21).

17. Give a brief account of the different systems of crystallography (22^.

18. Describe the different methods adopted for representing crystals (23; .

19. What are the ordinary positions adopted in representing crystals by
sketches? (24).

20. What is a crystal map ? (25).

21. Describe the difference oetween the orthographic and the stereO"
ffraphie projecUoDB (25).

22. what are crystal nets ? Draw nets for the regular octahedron and
the cube (28).

23. Draw the seven holohedral forms of the cubical system, and mark
the positions of the axes (30-36).

24. Give a tabular form of Miller's, Mitcheirs, and Naumann*s symbols
for each of the holohedral forms of the cubical system (30-36).

25. What are the limits of the deltohedron, the rhombic dodecahedron,
the three-faced octahedron, the four-faced cube, and the six-faced octa-
hedron? (32-36, 45).

26. Draw a sphere of projection for the cubioal system (37).

198 UINERALOGT.

27. Sketch the hemihedral forms of the cubical system, indicating the
positions of the axes, and giving liUUer^s, Mitchell's, and Naumann's sym-
bols (39-45).

28. Draw sis different combinations of holohedrBl forms in the cubical
system (47-48).

29. Draw six different combinations of holohedral with hemihedral
forms in the same system (50).

30. Draw six different combinations of hemihedral forms with each
other (51).

31. what are the P/0/o/}M;do<f«««, and what are their properties? Which
of them have been observed to occur in minerals P (53).

32. Describe the axes of the tetragonal system (55).

33. What are the angular elements of the tetragonal system P (58).

34. Describe the chief holohedral forms of the tetragonal system (57, 58} •
85. Define the terms prisM, pyramid^ and openfarmt^ as used in crystal-
lography (57-59).

36. Explain the order in which crystallographio symbols are placed in
combinations (60).

37. What is a sphenoid P (61).

38. Draw six hemihedral forms of tetragonal or ditetragonal pyramids
(62, 63).

39. Draw a sphere of projection for the tetragonal system (66).

40. Draw six holohedral tetragonal combinations, the principal asis
being placed vertically (67-69).

41. l)raw the same six combinations in vertical projection (70).

42. Draw six tetragonal combinations, showmg hemihednd planes
(71-73).

43. What are the axes and elements of the rhombic system P (74).

44. Show how the riff hi rh<nnhie pyramids and the derived rhomoie pffra^
mids are related to the rhombic pyramid hkl (75-77).

45. Show by a diagram the mutual relations of the rhombic prieme with
the maeropriems and brachypriems (78).

46. What are the symbols of the riyht rectangular pyramid and the
riffht rectangular prism ? (79. 80).

47. Draw six rhombic combinations, each of not less than three f onns,
and showing the symbols appropriate to each plane, placing the principal
axis vertical (81-85).

48. Draw the same figures in vertical projection (86).

49. Define the terms macrodome^ brachydome^ macropinaeoidf braehy*
pinacoid, and basal pinacoid (75).

50. What rhombic forms are mdicated by the symbols mh^L rhItL shklf
(87-90).

51. Draw a sphere of projection for the rhombic system (92).

52. Describe the axes of the oblique system (93).

53. What are the elements of the obhque s^rstem P (94).

54. Describe the principal forms of the obhque system (95-103).

55. Draw a map of the sphere of projection for the oblique system (103).

56. Draw six oblique combinations, and supply appropriate signs to the
respective faces (104).

57. Describe the axes of the anorihic svstem (105).

58. Describe the elements of the anorthic system (106).

59. Draw a map of the sphere of projection of the anorihic system (110).

60. Describe the axes and elements of the hexaoonal system (111, 112).

61. What are the chief holohedral forms of the hexagonal system P (113).

62. What are the chief hemihedial fonns of the hexagonal system P (1 19) .

EXAMINATION QUESTIONS. 199

63. Show the mntaal relations of the rhombohedrons with the scaleno-
hedro&B in the hexagonal system (l^^)-

64. Show the derivation of the rhombohedron from the double six-faced
pyramid (120).

65. Draw twelve hexagonal combinations, supplving symbols to the
zespective faces, keeping the principal axis vertical (125-128]).

66. Draw the same twelye combinations in vertical projection (128).

67. What is a macle, twin-crystal, or hemitroi>e P (129).

68. Define the terms twin^axu ana tufin-'plane as applied to macles ^29^.

69. Draw three macles commonly occurring in the cubical system (130;.

70. Draw two macles occurring in the tetragonal system (131).

71. Draw two macles occurring in the rhombic system (132).

72. Draw two oblique macles (133).

73. Draw two anorthic macles (134).

74. Draw four hexagonal macles (135).

75. What are the most commonly observed tmti'planea f (136).

76. What are the chief "iiregularities" of crystals (137).

77. Draw imperfectly developed crystals of alun^, spinel, and garnet (138).

78. In what minerals are curved " planes'' often met with P (139).

79. What do you know of striatum* and rouffhnesses on certain planes
of crystals? (140).

80. What are complex or poUynthetie crystals? (140).

81. Mention several of the most commonly occurring *' deceptive fonns *'
met with amon^ minerals (141).

82. What is dtmorphiem ) give examples. Give examples of trimorphiim

83. What is iaomorphiem t give examples (144).

84. What is polymerpus isomorphism? (145).

85. Oive examples of crystalline aggregates (146).

86. State what you know of psettdonu>rphi»m (147-150).

87. What is the difference between hypostatic and metaaomatic p86ad>
moiphBp (148-149).

88. What are anogene and hatoffene psendomorphsP (149).

89. State what you know of petrifactions (150).

90. What is a goniometer, and what is its user (152-154).

91. Describe Carangeot*s goniometer (152).

92. What ia the principle of Wollaston's goniometer? (153).

93. How would you proceed to read a crystal? (155).

94. What are the chief physical properties of minerals? (157).

95. What ere the principal directions of cleavage in the six systems of
crystallography? (157).

96. Mention six minerals occurring in the cubical system having perfect
cleavages i>arallel to the faces loo oo (157).

97. Mention six minerals in the tetragonal system having perfect cleaT-
ages, with the direction of those cleavages (157).

98. Do the same for the rhombic system (1^7).

99. Do the same for the oblique system (157).

100. Do the same for the anorthic system (157).

101. Do the same for the hexagonal system (157).

102. How would you distinguish by cleavage alone between xook-flolt|
linc-blende, and fluor-spar? (157).

103. What are false cleavages? (15Cn.

104. What are the chief varieties ox structure observable in minerals P
Give examples (159).

105. What are the chief Toxleties of fracture f Give examples (160).

200 UIKBRALOGT.

106. State what yoa know of the lelaiiTe tmaeity or frangtbUlty of
mineralfl (161).

107. How far may the sense of tonch be applied in «^i<Mtrtini«a^*ing
minerals P (162).

108. What is the *' scale of hardness/' and how maj it be applied in
determimng the hardness of a mineral? (163).

109. How would you distinguish rough fragments of rock-crystal,
diamond, and topaz, without the aid of chemicals P ri63).

110. If you had no " scale of hardness " by you, how would you deter-
mine apOTozimately the ^ hardness" of a mineral P (166).

111. What precautions are necessair to be obsenred in experimentally
determining the hardness of a mineral r (164).

112. How would you determine the specific gravity (a) of a mineral
lighter than water; (6) of a mineral heavier than water; {e) of small
fragments of a mineral P (168).

113. Describe Nicholson's araeometer, and the method of using it (168).

114. How would you determine the proportion of gold in a nugget com-
X)osed of quartz ana gold weighing 2 oz., the specific gravity of which is
3*4, without dettroying the nugget f (168).

116. How would you determine the specific gravity of a specimen of
xock-saltP (168).

116. What minerals havethe power of aifecting the magnetic needle P (169).

117. What is the difference between magnetic and diamagnetie sub-
stances (169).

118. 'De&nQihet&rmBpyrO'eleetrie md. frietio'eleetric. Give examples
of minerals to which these terms mav properly be applied (170).

119. What are analaaous and antilogous poles P (170).

120. State what you know of phosphorescence as regards minerals (171).

121. Define the teanns pyrO'phosphoriCjfrietiO'phosphorie, electrO'phoS"
phoricy and helio'phosphone, and give examples (171).

122. What are the chief optical properties of minerals P (173).

123. How far is colour a useful aid to the recognition of minerals P State
what you Imow of Werner's colours (174).

124. Define the terms pleochroiem, diehoroism, and triehroiim (175).

125. What is chatoyaneyy and in what mineral has it been observed P (176).

126. What is irideeeenee ? When it occurs in minerals, to what physical
phenomenon is it due P (177).

127. What is opaieeeeneey and in what mineral does it occur P (178).

128. State what you know of Jluoreeeenee (179).

129. How far is the streak of a mineral a useful guide in discrimination P
State the colour of the streak in three minerals (180).

130. What is the difference between the streak and the scratch of a
mineral P (180).

131. What are the varieties and degrees of lustre observable in nuneralsP
Oive examples (181).

132. What are the degrees of transparency or diaphaneity observable in
minerals P (182).

133. Draw characteristic crystals of garnet, galena, leucite, fluor, dia-
mond, tetcAhedrite, blende, boracite, pyrites, and cobaltite (chaps, v. to vii.)

184. What is *' refraction P " State the *' Uw of refraction/' and illus-
trate itbjr a sketch (183, 184).

135. What is ** double refraction P" What is the distinction between the
ordinary and the extraordinary ray P (185).

136. in what minerals may the phenomena of double refraction be best
observed P (185).

EXAMINATION QUESTIONS. 201

137. Btaiewh&tjoulaiow of polar isedUght. How may light be polar-
ised? (186).

196. Describe the tourmaline pincette, and the mode of using it (186).

139. What is a NicoFs prism, and how is it oonstructed P (187).

140. Make a sketch of a taole polariscope, and say what phenomena
may be observed by it (188).

141. How far are the optical properties of crystals dependent upon their
<;ryBtamne form? (185, 189).

142. What is a dichroiscope, and for what is it nsed P (190).

143. How far may the sense of taste be applied in the discrimination of
minerals? (191).

144. What minerals have distinct odours f (192).

145. In testing the eolubility of minerals, how would vou proceed, and
for what kind of phenomena would you be on the watch r (193).

146. What is the "scale of fusibility P" (195).

147. Mention six minerals which are insoluble in water, HCl, HNO^,
H2SO4, and aqua regia (194).

148. What are chemical elementt f Mention twelve of the most com-
mon, distinguishing gases, metals, and solid metalloids (198).

149. What is a chemical formula? f200).

150. How would you produce a reaudng flame and an oxidising flame
by means of the blowpipe ? (203).

151. To what series of blowpipe operations would you subject an un-
known mineral in order to determine its composition ? (204).

152. Mention three sul^tances which afford sublimates in the matrass.

153. Mention two minerals which decrepitate on heating (204).

154. Mention six substances which affoinl incrustations when heated on
charcoal, with the colours of the incrustations (204).

155. Mention six substances which tinge the blowpipe flame, with the
colours imparted (204).

156. How would you apply a solution of nitrate of cobalt in testing
mineral substances? (204).

157. What are the characters of the beads afforded by ores of gold,
silver, tin, copper, lead, and bismuth, when treated with carbonate of soda
on charcoal? (204).

158. What colours are imparted to beads of borax or tnieroeoemie salt
in OF and RF by copper, chromium, cobalt, manganese, iron, vanadium,
uranium, tungsten, and titanium? (204).

159. In heating minerals before the blowpi^ in Ft forceps, what phe-
nomena are to be looked for, and what precautions observed? (204).

160. Mention special and delicate tests for bismuth, boron, copper,
chlorine, fluorine, manganese, mercury, phosphoric add, and sulphur (205).

161. What substances may be best detected by means of the spectxo-
scope, and what is the method of testing? (206).

162. Mention six minerals which are commonly associated with —

0. Pyrites.

a. Quartz.

b. Apatite.
e. Casslterite.
d. Chalcopyrite.

/. Fluor.

a. Garnet.

A. Serpentine (208).

163. State the different ways in which crystals may be formed artifi-
cially, and give examples illustrative of each mode (212).

164. Mention twelve nunerals which have been formed artificially (Chap,
xxvii.).

165. State what you know of mineral ** growths" (220).

INDEX

Adamantine latire» 162.
Adamantoid, 88.
AffgregatM. mineral, 183.
Alamina, detection of, 184.
Angles, conitanoj of, 140.
Anorthic axes, 102.
„ elements, lOSL
„ macles, 123.
prisms. 103.
pyramids, 102.
sphenoids, 104*
sphere of projection, 101
system, 24, 25, 103.
Anorthotype system, 24.
Antimony, detection of, 184, 186.
Araeometer, 154.
Axwnio, detection of, 183, 184.
Artiiknal minerals, 191.
Axes, 10-25.

brachydiagonal, 25.
dinodiagonal, 25.
lateral, 25.
roaorodiagonal, 25.
orthodiMonal, 25.
principal, 2^

Barinm, detection of, 184.
Basal piuaooid, 50, 77.
Bismuth, detection o^ 184-189
Blowpipe, Blade's 181.

„ lamps, 181, 182.

„ operations, 183.
Borado acid, detection of, 184.
Borates, detection of, 184.
Borax bead, nse of, 185.
Bcvon, detection of, 186.
Botrroidal forms, 13.
Brachydiagonal axes» 2S.
Brachydome, 77.
BiBcbypinaooid, 77.
Braobyprism, 78, 7%

Carangeot's goniometer, 141.
GhatoTanogr, 161.
Cblorme, detection at, 186.
Chromimn, deteotioo of, 183w
Glsavage, 140.

„ iUsa^ 149.

„ ct roeks, 149.
Cllnodiagonal axes. 25, 93.
ClinorhcMmbio system, 93.
Gohalt, detection of, 186.

Cobalt solntion, nse of, ISi.
Colours of minerals, 160.
Colloids, 11.
Compounds, 180.
Combinations, 28.
Conchoidal fraotare, 150.
Cone in cone, 13.
Constancy of angles, 140-
Coralloidal frams, 13.
Copper, detection of, 185, 186.
Cryptoorystalline minerals, 12.
Cr}'stai maps, 29.
„ nets, 32.
„ drawings, 27.
Crystalline minerals, 11.
Crystallised mineral^ 11.
Crystallographic notation, 20.
Crystalloids, 11.
Crystals, artificial, 191.

cnrTatnre of, 128.

deceptive forms, 123.

elements of, 20.

imperfect development of, 126*.

irregularities of, 126.

measuring of, 140.

reading of, 144.

Btriations of, 128.

nsefal roles for, 145.
85.

foor-lkoed, 37.
Cubical combinations, 43.
macles, 120.
qrstem, 24, 34.

Cubej
Cube

Decrepitation, 183.
Deceptire forms, 128.
Deltohedron, 37.
Deltoid dodecahedron, 40.
Diaphaneity, 163.
Dichruism, 160.
Dichroiaoope, 171.
Dihexagonal prism, 109.

„ pyramid, lOSl

Dimetirio system, 24,
Dimorphism, 131.
Dipping needle, 157.
Ditetrsfunal prism, 59.

•.. »» . pyramid. 57.

DiTergent structure, 150.

Dodecahedron, deltoid, 40.

„ pentiwonal, 41.

„ rhombic,

„ trigonal, 40.

204

UINERALOOT.

>»

VcmtM, 82.

Double ■iX'ftoed prtom, 112-
„ „ pynunid. 111.

,t „ trapaxohedroii, 113.

,f ivftraotioii, 164.
Doubly oblique oombinatiinia, 113.

hemihedral forms, 110.
prism, 103.
pynunidi, 102.
sphenoids, 104.
sphere of projection, 109.
„ system, 24.

Drawings of crystals, 27.
Druses, 128.

Earthy fracture, 15L
Electricity, 158.
Elements of crystals, 20.
Even fracture, 160.

li'alse cleavages, 149.
Fibrous structure, 150.
Tluoresoenoe, 161.
Fluorine, detection of, ISO.
Fluoroid, 88.
Foliaoeous structure, 150.
FormulsB, 180.
Four4iaoeid cube, 37.
FkTictnre. 160.
Frangibility, 151
Fusibility, 176.

Oalenoid, 37.
Glimmering lustre, 1C2.
Globul&r forms, 12.
Gold, detection of, 185.
Ooniometer, Carangeot's, 140.
, Hannay's, 144.

O'Reilly's, 144.

„ reflecting, 141.

„ WoUaston's, 141.

dranatohedron, 86.
Oranatoki, 36.
Granular structure, 150.
''Growth" of minerals, 105.

Hackly fracture, 151.
Hannay's goniometer, 144.
Hardness of minerals, 161.

„ scale of, 161.
Heat, 150,

Hemihedral forms, 23.
Hemiortbotype system, 24, 93.
Hemiprismatic system, 93.
Hemipyramids, 88.
Hemitroiies, 120.
Hexagonal axes, 107.

„ elements, 107.

„ holohedral forms, 107.

„ macles, 128.

„ prisms, 109.

„ pyramids, 107.

,» system, 24, 26, 107.

Hexahedron, 85.
Hexakis octahedron, 88.
„ tetrahedron, 40
Holohedral forms, 23.
Hypostatic pseud<nnorphs, ISl.

loonhedron. 54.
loositetrahedrou, 37.
ImitatiTe forms, 12.
Incrustations on charcoal, 183.
Iron, detection of, 185.
Iridescence, 161.
Irregularities of crystal*, 12C.
Isometric perspective, 27, 28.
Iscnnorphism, 132.

•• polymeroos, 103

LameUar structure, 150.

Lateral axes, 25.

Lead, detection of, 184, 185.

Leuoitoid, 37.

Lime, detection of, 184.

Lithia, detection of, Ib-L

Lustre, 162.

Macles, anorthic, 123.
cubical, 120.
hexagonal, 123.
oblique, 128.
pyramidal, 123
„ rhombic, 123.
Macrodiagonal axes, 25.
Maerodomes, 77.
Maeropinacoids, 77.
Maoroprism, 79.
Magnesia, detection of, 134.
Magnetism, 157.
Mammillary forms, IS.
Manganese, detection of, 1S5, ISO.
Maps of ciystab, 29.
Matrass, use of, 183.
Mercury, detection of, 183, 180L
Metallic lustre, 162.
Metals, 179.
MetaUoids, 180.

Metasomatic psendomorphs, 185.
Micaceous structure, 150l
Mineral aggregates, 133.
„ "growths," 195,
Microoosmio bead, 186.
MineraU, artificial, 191.

brittleness, of 152.
colour of, 160.
exyptocrystalline, 12.
crystalline, 11.
crystallised, 11.
decrepitation of, 183.
definition of, 9.
distribution of, 191.
eleotro>phomhorio, 159.
fHctio-pbosi^oric, 159, 191, 195.
„ growths, 11.

hardness of. 151.
„ helio-phoBpborio, 159.

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Hinenuay pangenesis of, 188.

pyro-phosphorio, 159.

nlative age of, 190.

soooeasion of, 189.
„ toaoh of, 151.
Molybdates, detection of, 184.
Monoolinic system, 24.
Monoolinohedrio system, 98.
Monometrio system, 24.
Monotrimetrio system, 107.

Xets of crystals, 82.
Nicholson's aneometer, 154.
Nitrates, detection of, 184.
Nicol's prism, 109.|
Normals, 23.

Obliqne axes, 93.

„ combinations, 97.
elements, 93.
hemihedral forms, 95.
maoles, 128.
peendoprisms, 95.
pyramids, 93.
„ reotangalar prisms, 95.
», rhombic prisms, 94, 95.
„ sphere of projection, 9(S.
„ system, 24, 25, 98.
Octahedral system, 24.
Octahedron, 84.
Opalescence, 161.
Opaque minerals, 163.
Open forms, 94.
Optical properties, 160.
Orthodiagonal, 25.

„ axis, 98.

Orthographic projection, 29.
Orthotype system, 24.

Parallel perspective, 27.
Parameters, 19.
Paragenesis of minerals, 188.
Pear^ Instre, 162.
Pentagonal dodecahedron, 41.
FerspectiTe, parallel, 27.

„ isometric, 27, 28.

Petrifactions, 135.
Phosphorescence, 158.
Phosphoric acid, detection of, 184, 186.
Physical properties, 146.
Pinacoids, 59, 77.
Platonic bodies, 54.
Pleochroism, 160.
Platinum forceps, use of, 187.
Plenotesseral forms, 23.
PoJariscope, 169.

„ Table, 169.

Polarization of light, 168.
Polymerous isomorpnism, 183.
Poles, 38.

Positions of crystals, 28.
Potasli, detection of, 184.
Principal axes, 25.
Prismatic system, 24

Prism, Nicol's, 109.
Prisms, ditetragonal, 59.
„ rectangular, 79.
„ rhombic, 78.
„ tetragonal, 59.
Projection, orthographic, 29.
stereographic, 29.
sphere of, 81.
„ Tertical, 71.
FiMudomorphism, 184.
Pseudomoi^hs^ anogene, 185.

amphigene, 134.
esogene, 134.
exogen^ 134.
hypostatic, 134, 136.
katagene, 135.
„ metasomatic, 105.

^rnunidal maelee, 121.
„ system, 24.
F^mids« ditetragonal, 67.
rectangular, 79.
rhombic, 77.
tetragonal, 56.

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Radiate structure, 150.
Reading crystals, 144.
Rectangular prisms, 79.

„ pyramids, 79.

Regular octahedron, 34.

„ system, 24.
Refractive, 164.

„ double, 165.
Reniform, 13.
Resinous lustre, 162.
Reticulate structure, 150.
Rhombic axes, 76.

combinations, 24, 25.

elements, 76.

hemihedral forms, 8S.

holohedral forms, 70.

mades, 122.

prisms, 78.

pyramids, 77.

sphenoids, 88.

sphere of projection, 91.
„ system, 24, 25, 76.
Rhombohedral system, 24, 107.
Rhombohedrons, 110.
Rock formers, 10.
Rock masses, 10.
Rocks, 9.
Rocks, cleavage of, 149.

Scale of hardness, 161.
Scalenohedrons, 111.
Selenium, detection of, 183, 184.
Semi-tesseral forms, 23.
Semi-metals, 180.
Semi-transparent minerals, 1C3.
Silica, detection of, 184.
Silky lustre, 162.
Shining lustre, 162.
Silver, detection of, 184. 133.
Bix-fioed tetrahedron, 4a

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200

UIXERALOGT.

Smooth fi-actare, 151. *
Soda, detection of, 184.
Specific gntvity, 153.

,, bottle, 154.

Spectrotoope, 187.
Sphenoids, rhombic, 88.

„ tetragonal, 61.
Sphere of projection, 81, 04, OG, 104« 109.
Splendant lustre, 162.
Splintery fractare, 151.
Stalactitic forms, 14.
Stalagmite, 15.
Stellate straoture, 150.
Stereographio projection, 29.
Streak, 161.

Strontia, detection of, 184.
Stractnre of minerals, 150.
Sablimations, 183.
Sub-transluoent minerals, IQH,
Snlphnr, detection of, 183-186.
Systems of crystal forms, 24.

Table, polariscope, 169.
Tellarinm, detection of, 184.
Tenacity, 161.
Tesseral system, 24.
Tessular system, 24.
Tetartohedral forms, 23
Tetragonal, angalar elements, 55.

„ axes, 55.

„ combinations, 65.

„ hemihedral forms,

„ holohedral forms,

„ prisms, 59.

„ pyramids, 56.

„ scalenohedrons, 62.

„ sphenoids, 61.

„ sphere of projection, 64. 91.

„ system, 24, 25, 55.

Tetrahedrite, 40.
Tetiuhedron, 39.

„ six-faced, 40.

Tetrakis hexahedron, 37.

Three-faced octahedron, 86.
Three-faoed prism, 113.
Tin, detection of, 184.
Titanic acid, detection of, 1S5.
Touch of minerals, 151.
Tourmaline plate, 167.

„ pincette, 169.

Translucent minerals, 163.
Transparency, 163.
Transparent minerals, 163.
Trapesohedron, 40, 41.

„ twelve-faced, 40.

„ twenty-four-faoed, 40.

Triakis-oetahedron, 36.
Trichroism, 160.
Triclinic system, 24.
Trigonal dodecahedron, 39.
Trimetrio system, 24.
Tungsten, deteetion of, 185
Twelve-faced trapezohedron, 40.
Twenly-four-faoed trapezohedron, 40.
Twin axes, 120.

crystals, 120.

planes, 120, 126. f.

tt

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Uneyen fracture, 151.
Uranium, detection of, ISJIi

Useful rules for reading crystals, 145.
Veinstones, 10.
Vitreous lustre, 162.
Vanadium, detection of, 185.
VolatiUty, 177.

Waxy lustre, 162.
Woliaston's goniometer, 140.

Zinc, detection of, 1S4.
Zone axis, 23.

„ oirde, 23, SI.

„ plane, 28.
Zones, 28.

WILLIAM COLLINS A27D COMPANY, PmNTERSy C^LASGOW*